I was under the impression that "deleted" threads were still visible by moderators or other high-level members of the community. Is this correct? If a post was deleted that shouldn't have been, is it too late to bring it back?
Your impression is correct: users with 10k+ rep and site moderators can see deleted posts. No, it is not too late to resurrect them, unless some extraordinary action has been applied (like a lock). But you need some high-rep users to apply undelete votes. (I'm speaking here of posts deleted by the community.)
Information on how deletion works is here: How does deleting work? What can cause a post to be deleted, and what does that actually mean? What are the criteria for deletion?
We have a meta thread where some users request to reopen or undelete: Requests for reopen and undelete votes for on-hold, closed, and deleted questions