That's a little different than Claude doing the commits all by itself and happening to include an attribution line. Especially since, as it turns out, this was being done on clients that had all the AI stuff turned off. But even if that weren't the case, it'd still be wrong.
Also you shouldn't be using Claude that way...
I did this with the very first versions of claude which didn't have a documented setting to turn it off, and kept it every since. It works with every single coding tool because it just looks for the same key word.
This is not just a hypothetical but a non-common workflow: I already wrote upstaged code change myself. I ask claude to review it, and if ok, commit and push.
At no point did claude author any of it, just a review. So a co-author statement is false.