Interesting thread, and glad you mentioned Not Another Teen Movie. I really enjoyed that one, I watched it quite a bit with my roommate in college. I've found that it is typically unfairly lumped in with the shitty Friedberg and Seltzer films, despite them having no connection to it. My guess is, the title and poster style is similar to the Friedberg and Seltzer films. Not Another Teen Movie actually has closer ties to Zoolander, and Comedy Central.
Really, I think the spoof film genre went off the deep end when Friedberg and Seltzer fucked up the genre. In my opinion, a successful spoof film creates its own universe built off the back of a strong genre. Parodies aren't used literally, but rather are weaved in using the original characters created for the film. Look at Airplane!, The Naked Gun, Hot Shots, Austin Powers and Not Another Teen Movie. All of those are cleverly written, contain original characters (who themselves are parodies of existing character tropes) and have equal parts parody and original humor.
The Friedberg and Seltzer films, meanwhile, have very forgetful leading characters and lean far too heavily on direct parody, often cramming in reference after reference with very few actual jokes. In The Naked Gun we might see Frank Drebin in a situation similar to one seen in a cop thriller, but in Frank Drebin's case its played for laughs and they'll straight up poke fun at the ridiculousness of cop films. Friedberg and Seltzer, meanwhile, would just straight up hire look-a-likes for a scene pulled directly from a cop thriller, and would probably have somebody getting kicked in the nuts, or a woman whipping out her boobs, or have Mitt Romney appear in the scene for no reason other than it being "random".
Just look at home many great characters came from the successful parody films, and compare that to the Friedberg and Seltzer shit. I think it all comes down to writing and original characters. I'd take Austin Powers, Frank Drebin and Topper (Hot Shots) over the celebrity look-a-likes found in the Friedberg and Seltzer films any day.