Can I use TimeMachine with a Thunderbolt hard drive?
Yes. You can use Time Machine with any directly attached hard drive.  It is much faster, although if you have a laptop, it is somewhat less convenient to remember to plug the drive in than to use wireless.  

The folks from Apple were probably recommending a Time Capsule, which is a wireless router with a built-in drive for backups. It's definitely an easy way to do it, but not required.