Chicken comes out salty... occasionally
While this isn't a definitive answer, I've given it some further thought and believe that my original suspicion is probably correct.  That is, the saltiness is probably due to the chicken itself, and the kashrut is a likely root cause.

For the benefit of anyone unfamiliar with the koshering process for poultry, in a nutshell it involves removing the feathers and various other parts, then thoroughly coating it in koshering salt, which are flat, coarse-grained crystals that are ideal for sticking to the meat (unlike table salt crystals which would dissolve, or sea salt crystals which would just fall off).

The koshering process desiccates (dries out) the meat - the salt crystals absorb moisture, and then they are washed off, taking the moisture with them.  It's mainly done to remove the blood, but at the same time removes a lot of other moisture.  The entire process only takes about an hour and does not add a significant quantity of salt to the meat. Kosher salt crystals can absorb quite a bit of water before they dissolve and without being in a solution, they cannot actually penetrate the meat.

This is in contrast to brining, where the chicken is immersed in a saline solution and actually absorbs up to 10% of its weight in brine (which adds up to about 0.05% of its weight in salt for a typical solution of 5% brine).  This actually does makes the chicken saltier throughout, although very few people actually perceive this as "salty" - it just enhances the flavour of the chicken.

So if a brined chicken, which has actually absorbed salt, doesn't taste particularly salty, then a kosher chicken should definitely not taste salty, and normally it won't.  The caveat is that this assumes that the plant was diligent in its preparation of the chicken before packaging, and depending on where you live, many if not most kosher factories are anything but.

Specifically, there are a few ways a kosher processing plant could, by virtue of carelessness, produce chicken or other meat that's way too salty:


They can apply far too much salt to begin with;
They can salt it for too long;
They can wash it poorly or not at all.


All of these factors will compound each other leading to roughly the same effects:


The meat may become noticeably dry;
Crystals of salt may be deposited on the exterior, undissolved;
Over time some of those crystals may actually absorb enough water to dissolve, creating its own "brine" of sorts and even diffusing the super-saturated salt-water back into the meat.  Koshering is a time-sensitive process.


If you're also noticing any dryness in the meat then I would definitely think they were being less-than-thorough at the factory and suggest looking into different brands or even filing a complaint.

Even if that's not the case, or if you don't have that option, one thing you can probably do at home to compensate is to simply rinse the chicken thoroughly before cooking it.  Note that this is not for food safety, and rinsing a chicken is known to actually raise your risk (slightly) due to cross-contamination concerns.  But you are not doing this for food safety, you are doing this to get rid of non-bacterial contaminants (salt, and maybe other things) that the factory left behind.

Undissolved salt on the surface is definitely going to taste the saltiest since you'll be putting actual whole crystals on your tongue, and I think that's a very likely culprit here.  Salt and other solids really have a hard time penetrating the exterior of meat or poultry, so it's less likely for the salt to be inside the chicken, even if the processing plant was truly sloppy.

So try giving those kosher chickens a good rinse - don't forget to sanitize your work area when you're all done preparing them - and see if that helps you at all.  If not, then probably all you can do is find another brand or try to mask the saltiness with a lot of spices and sauce (find a recipe that's normally heavy on salt, and cut the quantity of salt used).

P.S. Note that this is quite speculative and I do not actually have first-hand evidence of this happening at a kosher factory.  Nevertheless, it is the best explanation I can think of for a kosher chicken coming out too salty when there is no salt at all in the recipe.  I've never had it happen with an unkosher chicken.