Firstly Archaeoptryx, I HIGHLY suggest you reconsider how you phrase your advice and telling people that they are "wrong", because as I'm sure you're aware (due to your mentioning of not using the MM model), there is more than one way to go about being a PUA. Sure, there are some things that you can say are "wrong", but they're few and far between, as you can basically act just about any way you like, just as long as you are doing things that attract women. Some guys will try a method and it doesn't work for them at all, but other guys do it quite well.
Personally, I use push/pull, but not in the early stages of a pickup, because unless you have built rapport, your push/pull isn't going to do anything aside from eject you from the set and most likely make it very difficult to get back in. Now, that's a general rule, not saying that you CAN'T use push/pull right off the bat, cause I have and it has been successful, but generally speaking that's what I've found.
Negging and push/pull do act in SIMILAR ways, but not the exact same, which is why it is important to know when to use which. Negging can work great right off the bat, I can walk up and say, "My god girl, you've got the most amazing dart throwing technique I've seen! You've got to play me a round, cause I broke my hand a while back and this is the first time I've found someone with an equal skill level!" Now that's gonna get her talking right away and maybe she'll hit me and get some kino going. If instead I were to walk up and say, "Wanna play a game of darts? Alright, I'll be back in a bit." She's probably not gonna wait around for me to come back, cause I haven't done anything to pull her into my frame and hook her.
Now, if she does something that I don't like, depending on my style, I could either neg her, or push/pull her and have basically (note the use of that word) the same effect. Say she talks with her mouth full, I could say, "I'm enjoying the conversation, but I understand you better when you swallow first sweetheart

" and she'll probably comply by not doing it anymore and trying to get back on my good side. I could alternately start talking with my mouth full in order to push her away a bit and hope she realises what's going on and why I'm doing it, or if the venue was right, say, "I'll let you finish your meal, then you can come find me."
Now, all of those, will probably result in her being polite and not talking with her mouth full, but it's gonna leave a different impression on her depending on how you go about it. Hell, there's millions of different ways to push pull and neg, so even once you pick which one you want to do, you still have the syntax to worry about, because even just the facial expression you make as you're walking away, or the tone in your voice when you neg her will change the outcome entirely.
Think about what response you want to evoke in your target and then choose your actions based upon that.