"Skipping over the finer details of how this probably isn't a "false accusation of criminal conduct",..."
Well, its a given that an accusation of copyright infringement is an accusation of criminal conduct, being that copyright infringement is against the law.
As for the accusation being or not being false, its very possible that it is false, especially if the criteria is that the party making the accusation must have a good faith and reasonable belief that the accusation is true. Under this system, if my ISP accuses me of copyright infringement, all they are basing it on is the copyright holder providing them with an IP address that they don't like, that happens to be mine. The ISP itself has no other basis for believing me to have engaged in copyright infringement except the word of the copyright holder. The copyright holder isn't providing them with evidence - it isn't even outlining what the evidence is. Its just the copyright holder saying "hey, the guy with this IP address is infringing! Trust us!". That's not exactly proof, or evidence, is it?
As for it being libelous or slanderous - (I forget which, but one of those is written / published word, the other is just spoken word), it depends again. Nominally the warning would be private. After all, they're just displaying a warning to me when I try to use my internet connection, right? Ok, now suppose someone is at my house using my computer or watching me use my computer when this warning pops up. Now, in their eyes, I'm a criminal. Now my reputation is damaged with that person. They may even spread the word. So the accusation is not private and for purposes of a person's reputation, might as well be public. There simply should not be a reasonable expectation that everything that appears on my computer screen is private and will only be viewed by me.