I think it is easy to say that Cyke pretty much in a state of hubris. What do you want Cap to do? Put it in writing and have a lawyer bring it over?
C'mon...Summers advisers at this point are Magneto, the White Queen and Namor - yeah they usually get it right the first time, even worse Namor is shown to be the one going "yeah this don't look good".
Some of this is just funky storytelling, as I think Cap would probably look to Hank McCoy for some science knowledge on the Phoenix situation, but they used Wolverine, as he is the bigger star character and obvious to use as he 'broke off from the regular x-men, putting him in the middle'.