This phrase gets thrown around all the time. I can't bring myself to believe that they actually believe what they're saying.
Joe Flacco: http://www.nfl.com/news/story/09000d5d82810e8a/article/joe-flacco-i-think-im-the-best-qb-in-football
I also heard Philip Rivers say it in lieu of his new contract during a soundbyte earlier today...
Colt McCoy said he was the best quarterback in his draft: http://www.cleveland.com/browns/index.ssf/2010/04/cleveland_browns_prospect_colt.html
As did Brett Hundley: http://jimrome.com/2015/02/13/brett-hundley-talks-nfl-draft-with-jim-rome/