You must have missed this:
But, in 2005, it was revealed in that W. Mark Felt, the associate director of the FBI, was Woodward and Bernstein's source. Furthermore, Haig was known to have been out of the country during some of the meetings between "Deep Throat" and the reporters.
Sorry, should have said was; I do remember that story coming out about Felt. My guess as the answer to your question about Haig feeling uncomfortable around certain people in Ford's administration was that at that time, he was one of the rumored possibilities as Deep Throat, and Rumsfeld and Cheney were Nixon camp.
Like I said, just a guess, thinking he would be uncomfortable around other Nixon followers when he was one of those having the finger pointed at him at the time...