May an emergency aircraft land on a closed runway?
Preflight Planning


  Let's say that you're on approach to a remote airport to refuel, with
  1-2 hours of fuel remaining in your aircraft. ...
  
  The nearest airport is 3-4 hours away...


First of all, it looks as if the pilot has already broken several regulations in order to end up in this situation.  He either didn't file an alternate, or if he did then he didn't carry enough fuel to get to it (and additional reserves as required).  If the runway is closed for an extended period of time, there would likely have been a NOTAM stating that the runway would be closed.  All of this sounds like poor preflight planning, and probably the 'ole careless and reckless thrown in for good measure.

The Problem


  Contacting ATC to request permission to land, they tell you that the only runway is
  closed for an unspecified reason and will not reopen for ~2 hours.


Okay, we need to figure out what the "unspecified reason" is because this can change things dramatically.


Is it for endangered migrating turtles?


Is it for construction?

In any case, he needs to use all available resources.  Talk to ATC and explain the situation. Ask them how they can help clear the runway so that we can land.  He should tell them that an emergency is imminent without their assistance.  They will do everything that they can to help you, including coordinating with people on the ground to get out of the way.  Be creative.  Did you know that there is no regulation (in the US) requiring you to land on an actual runway?  Ask them if you can land on the taxiway.  For that matter, land in the grass beside the runway.  It would be better than going for a swim or crashing after running out of gas!


  Let's presume the airport is surrounded by ocean, and the aircraft is not certified for ditching.


Ummm, who cares if it is certified for ditching?  If you are over water, it doesn't matter.  If you are over land, it doesn't matter.  If you have a choice, pick land (even if it's off-airport).


  Supposing ATC refuse to reopen the runway, is the pilot permitted to land anyway?


Well, they wouldn't really do this unless there was a really good reason, mainly meaning that it would be dangerous for the aircraft to land there (like in the second picture above).  In this case, we can't really ignore ATC and land anyway until:

Declaring the Emergency


  ...so you choose to hold, hoping the runway is soon reopened. After
  waiting a while, the runway is still not reopened, so you declare an
  emergency.


At least our poor pilot did this right.  Rather than blindly continuing to hold, he declared an emergency.  

Getting on the Ground

Now we have a lot more latitude and options, and ATC is better able to help us because they can pretty much do whatever it takes to save the aircraft.  This can change a "Sorry, there is nothing I can do." into a "Cleared to land any runway or taxiway." all on its own. They may throw in a "Landing at your own risk." if there are still hazards, but that's just to clear them of liability.  Even if they still refuse, you can simply advise them of what you will be doing and go ahead and do it.  Keep in mind however, that it may be better to scope out an off-airport landing site if the danger is so great that ATC won't allow you to land even under such dire circumstances.

Remember, the pilot is the final authority for safe operation of the aircraft.  Get on the ground and sort it out after the fact. (Poor turtles....)  

In the end, just do what you can to stay alive, and preferably use the airplane again.  There are going to be tons of questions and probably major legal battles.  Someone will probably go after the pilot's certificate.  On the bright side, he will be around to actually see it happen though.