This may be a dumb question, but here goes.

What if a player verbally commits during the summer between the junior/senior year and gets injured playing fall ball, or ridng his bike, or walking and chewing gum, or whatever? Let's say the injury isn't career threatening or anything, just a setback, like a scoped knee, shoulder, along those lines...

Does or can the school pull the offer off the table? Or is nothing official until he actually signs the NLI?

I would think they will make sure he is "good to go" when they sign the NLI-- it could make the waters a bit cooler for a bit

Verbal offers won't be official either. The NLI can't even be offered until the time of the early signing period.

Early signing period is November, correct?

Some players verbally committ during their senior year, not official until the letter is signed.
You might find this common when an older brother has played for the team or for an in state player.
I am to assume there would be no health issues.