Can you just confirm is this is the case? A bred true character is someone who possesses the same altered DNA from their parents, such as future Danielle Cage and Spider-Girl - they are not mutants because the DNA passed down isn't a mutation their parents went through, it is like them having the same coloured eyes? Whereas for Jean Grey's children to have the same powers as her and be a mutant is because she was a mutant? That being said, what is the case for 616 Daisy Johnson?
What you’re saying here is mostly correct. If Jean Grey’s chlldren had the same powers that she has, they wouldn’t be mutants in the truest sense (though they might still possess an X-gene), same as with Spider-Girl or Danielle Cage.
We know very little about the circumstances of Quake’s powers, so at this point I think it’s impossible to say.