Well, we have bantered about the semantics of what action is and how it relates to a check, but I believe that when these rules and RROP refers to action they are always referring to a bet or raise. And in this case it is a straightforward check by player A who has the option of a check raise when the action gets back to him. The fact that the all-in and subsequent call are short is meaningless to that players options. If there is a player who called and that still has more chips, player A can raise the pot. Now, player A has to raise it by the minimum bet so in this case he would have to raise it to at least $13.
Rule #38 only concerns itself with raises and therefore does not apply to the scenario that has been presented. In fact there is no rule that addresses this in TDA so you go back to RROP and Section 14:2 addresses this exactly: "...At all other times, when someone goes all-in for less than the minimum bet, a player has the option of just calling the all-in amount. If a player goes all-in for an amount that is less then the minimum bet, a player who wishes to raise must raise at least the amount of the minimum bet. For example, if the minimum bet is $100, and a player goes all-in on the flop for $20, a player may fold, call $20, or raise to at least a total of $120."