It does not. As I noted earlier, he will have some appeal process for this decision.
First of all, you are assuming something that you don't know: that the person was banned simply on an unconfirmed accusation of stalking. There may be more to it than you know. As others have indicated, the librarian may not have given him a full breakdown of what went into the decision in that conversation. Indeed, I would hope she would not do that in that setting.
Second, it is important to bear in mind that the library does have an obligation to keep the library a relatively safe place for library patrons. As such, it would not be wise for the library to simply ignore complaints by patrons that some other library user may be a threat. Could the complaint have been erroneous? Might the library have not done anything to confirm it before banning the guy? Certainly both could be possibilities. But neither you nor me know the truth of the allegations or the information that the library may have regarding it, so it's just not possible with what you do know to make a judgment on whether the library made the right call.
You can surmise, however, that if you were in the same situation as that guy (whatever that is) the library would likely take the same action.