There is no widely accepted, objective definition of either "role playing game" or "storytelling game".
A "role-playing game" is "a game where you primarily play a role"; "role-playing" is defined as "making decisions, from the perspective of the character". A "story-telling game" is "a game where you primarily tell a story"; "story-telling" is defined as "telling a story, as an author would". These definitions are descriptive, based on the meaning of words which are commonly understood. If you don't like them, then substitute in the sentence fragment wherever I've used the specific term, and it gets to the same point.
There might be some ambiguity, in many circumstances, but no sane individual could read the FATE Core rules and come away thinking that it puts immersion and role-playing ahead of telling a story. I could spend hours quoting the rule book on that point, but it would be a waste of time, because this is not in dispute.
The only dispute is whether FATE counts as an RPG, in spite of its obvious focus on story-telling rather than role-playing. That's just semantics, though, and doesn't change any of the underlying facts. FATE and other games with a strong focus on story-telling rather than role-playing are objectively distinct from traditional role-playing games. If meaningful discussion is to be had on the topic, then we need some sort of label to distinguish between them.
Once we have established a spectrum between role-playing and story-telling (or however you want to label them), then we can discuss
why I don't like Fail Forward, and we could further discuss how it might still be preferable given a suitably-distasteful alternative (even though Fail Forward is bad, it's not as bad as the players sitting around frustrated for four hours because they can't find a door). Or someone else could mention how they
do like Fail Forward, because their preference is more toward a collaborative story-telling experience rather than immersive role-playing. At that point, it comes down to a simple matter of preference. Evading the topic, by dismissing useful labels, doesn't get us anywhere.