Yes, it absolutely does support the sort of take on metagaming that I have. The DMG is against any and all thinking of the game as a game. Having a PC use knowledge that it doesn't have, but the player does is a form of thinking of the game as a game.
There are five whole sentences in that section. It's not hard to see what it does and does not say. It does not support your take on this subject. I leave it to others at this point to read that section for themselves and see how you are wrong.
Handle "metagaming" however you want at your table, but don't go looking to the DMG to validate your methods.
This is blatantly false. "Metagame thinking means thinking of the game as a game.", period. That's what it means. That is what DMs are directed to discourage and curb. Nothing in that section limits it to bad play experiences.
And in terms of thinking of the game as a game, it gives two examples at the heart of which are players doing things that lead to bad outcomes for them. Those are the instances of "metagame thinking" we are encouraged to avoid. It certainly does not consider "metagame thinking" to be "cheating."
Further, it says to discourage players from "metagame thinking" by asking "What do your
characters think?"
Excellent question! Because on page 66 of the Basic Rules, it says, "Roleplaying is, literally, the act of playing out a role. In this case, it's
you as a player determining how your character thinks, acts, and talks."
So, the player is the first and final arbiter when it comes to what a character thinks. The concern the DMG expresses over "metagame thinking" is to make sure what the character thinks isn't based on bad out-of-game assumptions that lead to poor play experiences such as underestimating a threat based on how the DM designs encounters or wasting session time on things that aren't important because you think the DM gave too much description on a particular thing. It has nothing to do with how to establish what a character knows. At all. A player is free to establish that his or her character thinks anything he or she wants. (Of course, what the character thinks may or may not be true!)
I make this post not for you - there's no convincing you of anything it seems. But I hope that anyone reading this and the section in the DMG (and the Basic Rules) can see that the game does not fully support your interpretation of this matter. That doesn't mean you're playing wrong. It just means the holy texts are not something you can use to justify your beliefs.