The 'speed' of conceding a game
As you have shown in your question, it is a house rule. That said, it's not a particularly surprising house rule as generally the kind of concession this would arise in could easily be a jerkish move, though not necessarily.

104.3a A player can concede the game at any time. A player who concedes leaves the game immediately. He or she loses the game.
101.1. Whenever a card’s text directly contradicts these rules, the card takes precedence. The card overrides only the rule that applies to that specific situation. The only exception is that a player can concede the game at any time (see rule 104.3a).
712.6. The controller of another player can’t make that player concede. A player may concede the game at any time, even if he or she is controlled by another player. See rule 104.3a.
405.6. Some things that happen during the game don’t use the stack.
405.6g A player may concede the game at any time. That player leaves the game immediately. See rule 104.3a.

Conceding isn't covered by the rules governing timing and priority. It is not listed in the rules under special actions. Rules as written; it can be done at any time, even when not in control of your own turn.