I'd say it's a database problem - nothing within UBB.Threads can corrupt the actual database. And your host doesn't seem to konw exactly what they are talking about, UBB.Threads is less intensive on the server than the "free" stuff like phpBB. The free stuff throws in every feature without much effort into efficiency. My guess they are mixing up UBB (Classic) and UBB.Threads.
Web hosts tend to say "we don't allow UBB" or "UBB is too intensive on the server" but they usually are thinking of UBB.Classic (flat file).