I've never tried to backup to a thumb drive, so I don't know whether it would do the same here.
I backup to the hard drive, then copy to a thumb drive. I do it that way because I want two copies of my backup.
And by the way, I use two thumb drives and alternate their use. So if you count a backup of the previous generation I have a third backup copy.
And every night, everything on the hard drive gets backed up to a different drive (using Windows Home Server). So that's a fourth backup copy. There are lots of things that would be terrible to lose, but my Quicken data would be the worst, so it gets the most copies.