Maybe it's Claude. I read in spoilers that we find out about Claire's real dad in episode 17!! We are on episode 13? ... Soo the whole OMG its shocking can still happen because we will get to know the Claude character and by the time we find out...we will be OMG shocked! lol.

The "Special relationship" or something that is rumored... it could be the fact that Claude is Peter's mentor and Claire is Claude's daughter...thats all.