Saints and philosophers wrestled with these issues back before there was television.  My recollection is that people who liked the idea of an omnipotent god would answer "omnipotence does not include the power to do nonsense" where they would generally include contradictions as nonsense.  So omnipotence can't square a circle, can't make 2=3, can't make an atom which is simultaneously lead and gold.  

But where do the contradictions end and the merely difficult to conceive begin?  Can omnipotence make the ratio of the diameter to the circumference of a circle = 3, or 22/7?  Can omnipotence make sqrt(2)=1.4 or 2+2=5?  While these are not directly self-contradictory statements, they can be used with a variety of simple truths to quickly derive self-contradictory statements.  Can we then conclude that "2+2=5" is essentially a contradiction because it is close to a contradiction?  Where do we draw the line?  

What if were set some problem where we are told to assume that 

1. 2+2 = 5
2. 1+1 = 2
3. 1+1+1+1+1 = 5

What if we set a problem where we are told to assume

1. Omega is an infallible intelligence that does not lie
2. Omega tells you 2+2=5

In Newcomb's box problem, we are told to assume that

1. Omega is an infallible intelligence
2. Omega has predicted correctly whether we will one box or two box.  

What if these statements are not consistent?  What if these statements are tantamount to assuming 0=1, or are within a few steps of assuming 0=1?  Or something just as contradictory, but harder to identify?  

Personally, I can think of LOTS of reasons to doubt that Newcomb's problem is even theoretically possible to set.  Beyond that, I can think that the empirical barrier to believing Omega exists in reality would be gigantic, millions of humans have watched magic shows performed by non-superior intelligences where cards we have signed have turned up in a previously sealed envelope or wallet or audience member's pocket.  We recognize that these are tricks, that they are not what they appear.  

To question Omega is not playing by the mathematician's or philosopher's rules.  But when we play by the rules, do we blithely assume 2+2=5 and then wrap ourselves around the logical axle trying to program a friendly AI to one-box?  Why is questioning Omega's possibility of existence, or possibility of proof of existence out-of-bounds?