Not sure about the specific plug ins they use, but I know MDDHosting was able to restore a MySQL table for one of my customers in about 30 minutes (that's from the time I submitted a ticket). I'm not sure if they actually restored the individual table, the entire database, or did a complete restore of the site, but the problem was solved, and I was happy.
The customer had changed the character encoding in MySQL thinking it would translate his blog into Hebrew.
We use the R1Soft MySQL module on all our shared / reseller servers. Like every host I imagine this cannot be done from the user r1soft option. So for us requires a ticket and escalation to our senior administrators to do any MySQL database related restores
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As Jedito stated you can purchase another Mysql agent for the customer so they can do it themselves, however in most cases this isnt affordable. We only use the one agent for the whole server on Mysql too.