an html file does not have anything to do with a php handler
I understand that, but the presence of the AddHandler line at one account and not the other does seem to affect how the primary domain at each account acts when an index.html file resides inside the primary domain's folder. At one account, it is ignored...and at the other, it is not.
All of that likely has to do with however BlueHost handles things, and I surely do understand BPS should not be expected to deal with that.