As explained in Episodes V & VI, part of the Narrator Rules is that they are not allowed to reveal Major Spoilers, which can change the entire course of the Story. The song "Too Close" also suggests that the Story of Central Park itself is intended to have a Downer Ending. However, Birdie is going to step in, since he knows how the Story is supposed to go through his time as narrator, in order to save the Park under Screw the Rules, I'm Doing What's Right! reasoning.
Central Park seems to deal with the Meta-narrative concept of the role of the narrator in a musical production, in a similar vein to Into the Woods or Pippin. The rules presented seem to imply that Narrators aren't allowed to interfere with a story already in place except in small, insignificant ways, such as giving hints or nudging the characters in the right direction, which seems to be shown when accidentally revealing a major plot point to Paige takes the role of narrator away from Birdie, but helping Owen and Cole out of the tree despite Griffin’s warning that interfering a second time could remove him from the story altogether gives him his role back.
Why is this? Well, the big difference between Birdie’s two moments of “interference” in the plot was the reason he interferes: the first time’s out of selfishness — he tells Paige the spoiler (even if accidentally) because he’s frustrated, impatient, and knows that Bitsy’s scheme will come to fruition by the time she ever figures it out on her own. The second time he interferes, it’s out of genuine concern and love — he just can’t stand idly by and allow two of his friends to potentially die, even if helping means the possibility of never seeing them again. This seems to imply that the narrator role does allow a narrator to interfere with the plot, so long as the decision to do so is based on unselfish motives.
Central Park has made it somewhat ambiguous as to what Birdie can and cannot do or know: while he knows everything about the story, he has to still figure out what each character knows, and it's implied the main reason he knows some of what he does about the Tillermans is because he spies on them. He's certainly not omniscient, but as a narrator, the role he plays is generally outside of the story: he just happens to also be in the world with the characters. However, none of the rules provided in the list shown during "Spoiler Alert" directly say a narrator can't change the story, simply "no spoilers". By saving Owen and Cole, Birdie did not break any rules, but —by virtue of changing the story by saving them— has become a part of it himself, and is reinstated as narrator to keep his character within the story to prevent something akin to an in-universe Died During Production, as opposed to Griffin, who has done nothing at all and is ergo expendable. Notably, Griffin agrees with Birdie that while narrators are allowed to interact with the story and the characters in order to gently nudge the story along, the characters ultimately make their own choices- in his eyes, a narrator getting "too close" to the characters leads to the narrator getting too invested in them and jeopardizing their free will (which Birdie nearly did with Paige); and therefore they should instead allow the consequences of the character's actions, good and bad, to take their natural course, even if it means letting them get hurt by said choices. This implies that this is allowed in some form; it's just that they didn't realize "no spoilers" and "don't interfere" are not the same rule.
It would be the ultimate irony — after all that time trying to get rid of Shampagne in order to inherit everything, she succeeds in getting the inheritance... only to be stuck with Shampagne in order to get any of it.
- To be fair, Helen mostly seems to hate Shampagne as an extension of how much she hates Bitsy, being forced to run inane dog-related errands and clearly being way, way below Shampagne in Bitsy's estimation. After all, Helen didn't ultimately didn't go through with her plan to get rid of Shampagne when she could have, even if it was just barely, and she knows that Cole is more than willing to take care of Shampagne; if the above happens, Helen would probably just hire Cole as a full-time dog-nanny or something and everyone would be happy.
... in Season Two, as the Narrator of another story that intersects with the Birdie-narrated story of the Tillermans. This will either bring them into conflict again, as they try to make their own narration (and the ones they're narrating for) take precedence, or will result in a reluctant co-narration until the storylines diverge.
He interfered in a previous story he was narrating and it ended badly: Maybe it got him transferred away from people he'd grown attached to or resulted in a Downer Ending that wasn't supposed to happen, or maybe the Bad End he was trying to avoid came to pass anyway and he became disillusioned with trying to change stories for the better. Whatever the specifics, it was enough to convince Griffin that the best thing a narrator can do is to stand back and let the characters make their own decisions, even if said decisions would lead to unpleasant outcomes.
