At first, yes, but I think it is right

It would seem going second gives the advantage of "knowing what you need", but going second in the NFL means if you match each other, the other team now gets first possession in sudden death. (Basically what Shanahan said.)

Most folks are assuming a TD by the first team. If that is known, then yes going second is smart. But if we assume the first team gets a FG, then the second team will likely kick to tie vs a 4th down (when in range) in their possession. So you would definitely rather be first if you knew FGs would be exchanged.

It seems there are a fair number of interesting permutations.