Here's the thing -- as a player, you don't have the ability to insist that your reading of the rules is the correct one, even if there is no significant difference between your reading of the rule and the text of the rule itself. The ALPG has noted since the beginning that "[a] DM's ruling at the table is considered final for the purpose of that play session." The DM is always right, even when the DM is demonstrably wrong.
So the idea that "the DM is not playing by the rules" is itself flawed -- the DM is the only person at the table who has the authority to decide what the rules are for that play session. It is true, though, that if you find yourself constantly in disagreement with a DM over what the rules are, you probably should at the very least try to avoid sitting at a table with that DM in the future, and if it gets really bad, then withdraw from the event, taking no rewards from the adventure.
I will say that, in my experience, pointing out a rules reference to the DM from the actual Player's Handbook usually solves any disputes, since most DMs do want to run games according to the official rules. However, just because you have a specific interpretation of how a given rule works (such as Acrobatics to try to trip enemy combatants), the DM is under no obligation to agree to your interpretation, especially if she feels the result is abusive.
I've had DMs tell me that sneak attack dice are not doubled on a critical hit, that darkvision doesn't work without a light source, and that the Spare the Dying cantrip failed when used on a clearly dying but not yet dead NPC. I've learned that I tend to enjoy play sessions more when I let those things go and focus on what's coming, rather than fighting a battle that I don't have the authority to win and then letting that frustration color the rest of the game session.
'Expect table variation' is not just good advice, it's a way of life.
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Pauper