Well, this is Ian O'Connor, so large grains of salt have to be taken. However...
I wouldn't dismiss the "BB 'didn't believe' Brady" one out of hand.
Remember BB's initial "well, you'll have to ask Brady about the balls" response when it first broke. Didn't try to defend Brady at all. To this day I think that in the first couple of days BB didn't believe/trust Brady and wasn't willing to put himself on the line by saying anything like "Tom would never do anything like this", especially because if he did say something like that and it turned out Brady had done something, Goodell would use it to crucify him.
Then after the first day or two I'm sure Patricia (and maybe also Cam Fleming who was an aero/astro from Stanford) told him about the IGL and there was probably some big powwow leading to the Mona Lisa Vito press conference.
Now, the "Brady thought Spygate was 'likely true'" is dumb because BB never denied the filming so of course it was true (in the sense that the Pats had been filming teams). Or is O'Connor saying that Brady thinks Tomase's story was "likely true"?