I have a few thoughts on this, from benign to worst-case.
1) They're OCD (but you can usually tell this if they've labeled their paperclip and thumbtack drawers.... true story)
2) They're germ-freaks
3) They're unaware of why you are working on their computer.
4) They're concerned (un-necessarily) that you will find something in/on their desk/computer
5) They're concerned (with good cause) that you will find something in/on their desk/computer
Honesty is always the best approach, however. Humans can be territorial, and even though they know (in the back of their minds) that it's not THEIR computer and THEIR chair, they still feel threatened by having their private area invaded.
Sometimes the best approach is to talk to them (using "I" language if necessary and a smile) and point out that you're not there to snoop on them, but for the safety of the entire network / company assets / bla bla you needed to make sure that backups are running correctly. Remind them that they would lose THEIR data in the event of a failure if their machine wasn't backed up.
Reminding a person that it's not "Their" stuff or "Their" cubicle is never a good route. They know that; and reminding them of that weakens their comfort level with their job.
If it *does* escalate to a supervisor or whatever, please PLEASE remember that the goal of any kind of "corrective action" or "redirection" should be a better employee; and not to "put someone in their place".
Just my 2¢
"What the captain doesn't realize is that we've secretly replaced his Dilithium Crystals with new Folger's Crystals."
--Greg