I think the "college coaches can't succeed in the NFL" thing is overblown a bit.
The biggest difference is that many top college coaches aren't actually that good at coaching; they just have a lopsided talent advantage that gives them a "big name" in the sport. Give Dick Jauron a Pro Bowl roster comprised of the best AFC and NFC talent put together and he's going to rack up a lot of wins vs the Lions, Giants, Jaguars of the league, especially if he gets to have a hand in crafting his schedule to his advantage. The he plays the Bucs and loses and "just can't seem to win the big one" but his record is still really good and everyone pumps him up as a top guy.
That said, there are many really good college coaches who would succeed in the NFL. Ball is ball. People are people. Of course there are differences, but we're not splitting the atom here; it's football and working with people.
Chip Kelly was 26-21 in Philly in 3 years, which is a winning record. SF was a disaster when he went there. That was hopeless for anyone. Chip's issue was wanting to control everything the way you can in college, but he did pretty well I think as an NFL HC in Philly outside of the personal relationships (which of course are a big part of the job).
Nick Saban had a lot of NFL experience as a member of Belichick's staff in Cleveland, so he knew the game. He had no QB, which makes NFL football no fun. I think if he had a passion for NFL coaching he could do it and be very successful. Why would he, though? He's a celebrity on campus, always wins, and gets the best players.
Jimmy Johnson was a ball coach. The guy knows football AND knows how to work with people. A lot of times these big name college coaches lack one or the other of those skills, because on campus you're a legend and your word is the word of God in some of these places. It's your players who you recruited who are there because they idolize you and will do whatever you say.
AND you have a huge talent advantage most weeks.