Actually Fedor has turned down a few fights. He turned down a fight with Cro Cop in PRIDE (Shockwave 2003) to fight Yuji Nagata at Inoki Bom-Ba-Ye back in 2003 (both shows happened the same day). Which is why PRIDE set up an interim HW Title match between Big Nog and Cro Cop the following month. It's worth noting that Mirko Cro Cop was undefeated at that point.
Fedor also turned down a fight with Vitor Belfort at Affliction: Trilogy after Barnett tested positive. Vitor wanted the fight, Affliction offered the fight but Fedor and his management wanted to fight Brett Rogers instead. Which is why Affliction ended up contacting Strikeforce to get permission for Rogers to compete (since he was under contract with Strikeforce). That's when Fedor stated in an interview with Sherdog that he prefers to fight bigger, slower HW's and that smaller, faster guys have always been harder to fight for him. He also said there that he would prefer to fight Brett Rogers. Vadim (M-1 Global) said the same thing.
And in Strikeforce Fedor turned down Overeem. Scott Coker wanted Fedor to fight Rogers and THEN Overeem for their HW title. Fedor refused which is why Overeem fought Rogers (who Fedor just beat) and why Fedor fought Werdum yesterday.
Care to elaborate? And I made a mistake..

Shogun is supposed to be #5 on my list.