Strange question but does the user own those files ?
if you login by ssh and type ls -al in the users dir where he tries to delete files, is the username and group the same as /home/<what you have here> ?
If not you can try chown <username>:<username> -v *, just watch out jou DON'T do this in /home/<username>/ but do it in /home/<username>/public_html or another dir.