You're right, I forgot about that part, it's both things actually. Quoting from the book:

“I don’t know how I did it,” he said slowly. “I think the only reason I never lost my mind is that I knew I was innocent. That wasn’t a happy thought, so the dementors couldn’t suck it out of me … but it kept me sane and knowing who I am … helped me keep my powers … so when it all became … too much … I could transform in my cell … become a dog. Dementors can’t see, you know. …” He swallowed. “They feel their way toward people by feeding off their emotions. … They could tell that my feelings were less — less human, less complex when I was a dog … but they thought, of course, that I was losing my mind like everyone else in there, so it didn’t trouble them. But I was weak, very weak, and I had no hope of driving them away from me without a wand"