and now we are back to whether or not a check is "action" in the sense that it is used here. So let's see if RROP can't help us out here. Let's go to the glossary of RROP and look up the terms 'Action" and "Check":
ACTION: A fold, check, call, bet, or raise. For certain situations, doing something formally connected withe the game that conveys information about your hand may also be considered as having taken action. Examples would be showing your cards at the end of the hand, or indicating the number of cards you are taking at draw.
Ok, so a check is action. A player who checks can be considered to have acted. But what sort of action is a check?....
CHECK: To waive the right to initiate the betting in a round, but to retain the right to act if another player initiates the betting.
So this says that while a check may be "action" it is a specific type of action. One that gives the player the right to "act again" if an opponent initiates the betting. But let's go a little further because what we are really discussing here is whether player A can actually raise once action comes back to him, or "Check-Raise".....
CHECK-RAISE. To waive the right to bet until a bet has been made by an opponent, and then to increase the bet by at least an equal amount when it is your turn to act.
Wow, to you see the last bit there where it says you have the right to act again? And you get to increase the bet by at least an equal amount this time!!!!
How do you reconcile what you read in rule 3 (under RROP sec 14) about a player who is " not facing a full size wager may not subsequently raise an all-in bet that is less than the minimum..." with what is in rule 2 of the same section that says "if a player goes all-in for an amount that is less than the minimum bet, a player who wishes to raise must raise at least the amount of the minimum bet. For example, if theminimum 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"



?
The only apparent difference between player C, who according to rule 2 can raise the short all-in, and player A, whom you claim cannot, is that you say player A has already "acted". And this is where I believe that the term can have a different meaning here. I believe that "acted" here refers to a player that has already put a wager in the pot. I can demonstrate this by using our example again but rather than a short all in we use an all-in that is just above the minimum bet.
So, player A checks, player B bets $10, player C goes all-in for $13, action is now back to player A and I know you will agree that player A can Raise to $23 at least.... But what if player A decides to just call the $13? THEN PLAYER B WOULD NOT BE ABLE TO RAISE BECAUSE HE HAS ALREADY "ACTED" (BY BETTING) AND CANNOT RAISE THE SHORT ALL-IN BECAUSE HE IS NOT FACING A FULL SIZE RAISE!!!! That is what rule 3 is referring to. NOT TO THE CHECK RAISER of a short all-in initial bet!!!
Do you see how those rules are related? And how the term "action" is being used differently?
btw - check out rule 4 in section 14 as it gives the example above, essentially.