Well, I've been going back and forth with the ISP on this one... they did make some progress. It now gives a new error message but also says the database has been saved. Here's the error:
0 => mysqldump: Error: Couldn't dump tablespaces SELECT command denied to user 'rvallee'@'souari.forest.net' for table 'files'
Success: The database has been saved.
And this is the message Tech Support sent me:
I've updated the mysql client libraries and we no longer get a core dump:
[here they quote the messages above]
Is there any particular reason this specific table would have stricter permissions? It does seem to have dumped about as much data as could be expected, but I'm not sure if this particular table has always given you an error or not.
Since my database knowledge is totally basic, I have no idea how to even answer this question. Any suggestions or ideas about what this means? Is my entire DB actually being backed up now?