Is it safe to cook large cuts of meat sous vide?
Generally speaking, to answer the final question in the post, i.e., "It is sometimes unsafe to cook large cuts of meat using sous vide techniques," the answer is assuredly, "Yes, it is sometimes unsafe."

The problem is that it's difficult to identify precisely when it becomes unsafe.  That's why the USDA guidelines are so strict: they are meant to be simple rules that apply even under really non-ideal circumstances.

What are the factors to consider?  Well, the thickness itself is only a small part of the equation.  The numbers cited from Douglas Baldwin in comments and in Stefan's Gourmet linked in another answer are grossly oversimplified to the point that they aren't much better than the USDA blanket recommendation.

I mean no disrespect to either of those sources here, because both are valuable.  The Stefan's Gourmet link simplifies the approach of the book Modernist Cuisine, which is itself an oversimplified view of microbiology.

I'm not a microbiologist, but I have taken courses related to it.  I've also taken courses related to heat transfer, and I've done basic numerical modeling on how you'd have to look at heat transfer in a large hunk of heterogeneous material.  It's incredibly complicated.  The equations that are used to generate tables used in those links are already rather complicated, but they are based on a lot of assumptions -- the important ones here being (1) symmetrical shape, (2) homogeneous composition of material, and (3) a specific thermal profile of that (fictitious) homogeneous material.

In plain English, those tables basically treat a turkey as if it were a giant sphere (or cylinder) of X, where X is a magical substance that is chosen as an "average" of the various components of "average" meat.

Compare that to heating an actual large piece of an animal, like a whole turkey.  Muscles vary in their density, which changes thermal properties.  Veins of fat or connective tissue have their own thermal properties, as do bones.  Bones might serve as speedy conductors of heat energy in some cases, but might slow down heat transfer in other situations.  

What's the temperature of the water bath?  How far is it above the danger zone? 
 That's also not something reflected in some simple charts.  What you care about is how much time it takes the meat to get over around 130F, not how long it takes to get within 1 degree of the water bath temperature (or whatever the desired outcome).

And then you have the problem of air, as in the cavity of a turkey -- which is a huge issue in however you cook a whole bird.  Air often acts as an insulator, though it can be used with convection to transmit heat more effectively.  In a sealed sous vide bag, though, most of that air is likely to just sit in there, getting in the way, along with the bones and other stuff that will have all sorts of impacts on heat transfer.

That's why Douglas Baldwin wisely tends to stick to thin steaks or whole cuts of muscle tissue, as they will be somewhat more predictable.  Modernist Cuisine and its followers take a more cavalier approach to food safety, basing their recommendations largely on Salmonella death computations.  The latter were originally chosen by the USDA many years ago to model food safety, as Salmonella is often the fastest growing pathogen in relatively quick-cooking methods (as recommended by the USDA).

But the USDA (and Salmonella death rates at various temps) are not enough to the toxin problems in something like a turkey cooked for a very long time in the "danger zone."  At that point, you'll kill off the Salmonella just by heating above the danger zone for long enough.  You can easily ensure that in a sous vide situation.

However, the problem with something like a large turkey isn't going to be Salmonella -- it's going to be so-called persistent toxins produced by rapid growth of other types of bacteria at elevated temperatures in a water bath (though not hot enough yet internally to kill bacteria off).  These persistent toxins may require higher final temperatures to denature the toxins and render the food safe to eat.  In some cases, the temperatures required to destroy such toxins might be high enough that the advantages of sous vide would be lost.  In other cases, the overgrowth of bacteria during cooking in the danger zone could leave large numbers of bacteria in spore form, which will begin to grow again after cooking, leaving the food safe to eat immediately, but unsafe for leftovers.  (That's probably a concern when you're cooking a large hunk of meat -- you often want to be able to use leftovers.)

None of this is really answering the question directly, because it's really hard to give appropriate guidelines without falling back on some "rule of thumb" like the USDA.  Based on the USDA's own advice for cooking meats like large turkeys from a frozen state or smoking meat at low temperatures, I know they find it acceptable for some parts of the meat to be in the danger zone for longer than two hours.  But how long is too long?

Some people, for example, cook a Thanksgiving turkey "low and slow" overnight at 200F in the oven.  To me, that's a bit too risky.  (Though I might do a modified recipe where the turkey spends time in a hot oven to brown first, "jump starting" the internal thermal gradient to get it to temperature at least a little faster.) 
 Putting a whole turkey in a sous vide bath at 165F or something would probably get it out of the danger zone quicker than that, so while I wouldn't cook a turkey that way myself, it's probably safer in terms of statistical likelihood of danger than some methods people already use.

Some of the risks can be mitigated by searing exteriors of whole cuts in advance (to kill surface bacteria), restricting sous vide to relatively homogeneous cuts of muscle, and/or cooking at a higher temperature for an initial portion of the water bath before turning the bath down to the final desired temperature.

But honestly, I'm not going to mess with any of that.  Sous vide has its greatest advantages when it can cook evenly -- one might say that's the main point of sous vide cooking.  A whole turkey or a whole chicken is not going to cook evenly in a sous vide bath when it spends a large amount of time at different internal temperatures.  In fact, with the large amount of air that will remain in the cavity, it is even sous vide (i.e., "under vacuum") anymore?  

So, cut the turkey or chicken into pieces.  Bag them individually.  You'll get a superior result, I'm sure.  In addition, you could do what's most appropriate and cook the dark meat to higher temperatures in your bath than the white meat.

For large roasts of other animals, I'd consider cutting them up in they were oversized.  A prime rib is probably not going to have as much internal bacteria to worry about as a chicken or turkey, but it still will heat unevenly due to mixtures of lots of fat and muscle as well as bones.  Still, I've done a boneless rib roast in sous vide and would do it again -- but that seemed thin enough to me to not worry about the transient heating issue.

Bottom line is that sous vide is probably just as safe if not safer for large hunks of meat as other super "low and slow" methods people sometimes use in the oven, etc.  But those latter methods are themselves probably not very safe in some cases.  When I look at charts in those links and see that under ideal conditions with a perfectly homogeneous hunk of meat it might take more than eight hours to get through the danger zone in the center -- I might start to think twice about a recipe.  And I might start looking at the final temperature more closely: will the meat get to a high enough temperature to kill off bacteria and denature possible toxins that accumulate over several hours?

There's no simple answer here, but I wouldn't trust any recipe or table of values telling me to cook something for more than about four hours without understanding the assumptions it is making and the food safety model it is based on.