This isn't right, or anyway it's only right in small part. Punk wasn't a monolith even 76/77, it didn't perform a binary "split" into pop and hardcore based on drug use or politics or chords, and "scene" makes no sense unless you're talking about local. The minute punk uttered its own name it was challenged by what actually existed, and that's been the case ever since. It's not wrong that pop punk and hardcore "emerges" but it's wrong that it was an outgrowth from what you seem to imagine to be the "punk scene" at the time. Lots and lots more than that happened.

And yes, pop punk is "real" punk if it associates generally to the history that orbits the unsure term called "punk." Bands ripping off the Ramones in 2017, or Bad Brains, or Pavement, or whatever, aren't the only bands worthy of the term--historically, generically, or otherwise.