Talking about hole cards after hand is over

[DrMcNasty]

The following situation came up at a tournament game at a local lodge (legal; they don't rake or take a cut and you don't have to be a member). I'm curious about comments and where to look for a definitive answer.

Everyone folds to the button who limps, I raise from the SB, the BB and button call (3-handed). The flop is 3 hearts and I don't have one so I check, the BB checks, and the button bets the pot. I fold and BB folds. The button takes the pot. I speculate about the BBs hand (not directly asking what he had but looking for info) and the BB says AhXx. The button objects, saying that I now know what the button *didn't* have in that situation (sort of sharing information on a player's tendencies).

Three questions:

(1) Was I out of line to speculate on just one (or any) of the hands?

(2) Was the BB out of line to say what he had (he didn't show it... he could have been lying)?

(3) Was the button objecting without justification (remember, the hand was over and the next hand hadn't begun)?

My sense is that it's OK to talk about a 3-handed pot once it has concluded... I've never heard anyone raise the objection before. Yet I'm having a hard time finding a guideline that indicates that either I or the BB was out of order.

Thanks in advance for your help.