Guillaume,
I think we need to establish a firm rule. Without a verbal declaration, placing too many chips into the pot, will be considered the intended amount of a wager. This will include; failure to retract a lesser amount i.e., a blind or lesser amount from the current betting round, while adjusting your intended wager.
In your recent example: Once Player A checks after the flop, I would rule his hand dead. This can get tricky because if Player A were attempting to call, he should have spoken when he realized the dealer was about to burn and turn prematurely. By his check, I can only assume he is trying to see the turn and river at a 3000 savings. If he tried to stop the dealer before the premature flop, that's a different story. The dealer would announce to the table that the current flop can not remain. The option would be extended to the skipped Player A, where he would be allowed to fold (surrendering his 2000), call the additional 3000, or even raise. I, however do not like the option allowing him to raise but, that is the way the rule is written.
I like to compare this situation, for NLH, with a player tossing a single 100 count chip into the pot when the amount required to call is 25. As we know, his action is only a call. Take the same betting round, except the initial bettor tosses a 100 count chip...the bet is now 100. Players must learn to make their intentions clear, whether betting or calling or raising, too. Without explicit rules, players will always be at the mercy of the "floor."