The only time I ever had members of the Companions go aggro on me was when I had unwittingly done something that got me a bounty in Whiterun. The Whiterun guards didn't acknowledge it, but when I went up to Jorrvaskr the Companions who were out back in the training yard attacked me as soon as I came around the corner and was noticed. Some (maybe all) members of the Companions are tagged as guards, and they will go after you if you have an outstanding bounty.
It's a known issue that you can have a bounty that is not recognized by guard NPCs but is recognized by others who are in one of the "law enforcement" factions. That includes members of a Jarl's court, I had the same thing happen in Windhelm... somehow aquired a bounty in Eastmarch. The guards there didn't get the memo but when I entered the palace I was immediately attacked by Galmar, Ulfric, and the Thrice-Pierced (?) guy who also hangs out there.
In both cases I had to do some minor crime to add to the existing bounty in a way that the guards would respond to, but that didn't make it so serious that I couldn't just pay it *all* off with my available funds. Once I was allowed to pay it off, though, it paid off every outstanding crime and I was free and clear.
I did it by trying to pickpocket the first lone guard I encountered in the relevant city/hold, with any followers stowed away somewhere out of range, just in case things went really sour. And I did a save first just to be extra sure, lol. Had lousy pickpocketing skills so in each case the guard immediately tumbled to what I was doing and gave me the "halt" order or whatever they do and then I took the option to pay off my bounty.
Probably wouldn't work if the situation is such that just paying things off is no longer an option, but it's worth a try.