alt Hacker NewsIAAL (not legal advice) and I’m not sure the issue is settled.
The BSD license only explicitly permits the author “to use, copy, modify, and distribute this software and its documentation for any purpose, without fee, and without a written agreement.”
By default, the owner of a protected work retains all rights not conveyed to someone else. Changing the license isn’t one of the enumerated activities, and so I think there’s a case to be made that it’s not permitted.
Now if the author wants to claim it’s a new work, as opposed to a modification (which opens up a big bag of issues by itself because this was AI-authored), then the author can license it however they see fit.
You are not really changing the license of the original work though. You are not impacting what the author or anyone else can do. You are distributing a copy under different, more restrictive terms.
A bit like me buying a comic book, then offering to sell it to you under the condition that you never let my brother read it and that you make any future owner agree to the same terms. That's perfectly legal, and there is no reason I would need permission from the author (or publisher) to do that