Ironic, I had a situation like this just last Friday. As the systems admin the work didn't even fall into my sphere. Like SondraGail I used the Socratic method, then double checked what the coworker had been doing that required me to handle their work. It turns out they were accessing...ahem..."prohibited websites" when they should have been working. Just because you clean out your browser's history doesn't mean you've cleared the activity logs. The coworker also got a virus into the system I was able to nuke before it did anything. When I passed all that onto their boss, she went volcanic on them. The ducts do an excellent job of carrying voices where my office is, so I got to hear the entire thing. I won't repeat the conversation but it did end with two words: you're fired.
Way-back co-worker used to do a version of this only it wasnt about work issues - it was about her unverifiable *personal space* issues.
She complained to manager/HR that others shouldnt wear perfume or colone due to her smell sensistivity. She complained about her phantom back problems to get a very expensive special chair out of the budget. She complained that certain people talked too load and disturbed her. She had bad cramps every month that made her have to take off a Friday/Monday or both. EVERTHING gave her migranes.
Our male manager/HR people cowered to her control-issue demands out of fear - what would now be a contrived episode of The Office was our daily reality. I forget what our real jobs were - walking on crazy-lady eggshells was the order of the day.
On one of her monthly Friday cramp-vacations - myself and one trusted compatriot stole her precious chair and buried it in a great pile of stored office equipment in a far-off building on the other side of the campus. <pre-security cam days>. The ensuing s h i t storm was something to behold - took a special security detail to find the chair after four days.
Nothing changed, and we were all suspect, but office work is sadly only about the little victories...
Ah, the memories. A cow-orker tried this on me once. When my boss brought her 'request' to me, I used the Socratic method. Whose responsibility is it to do that work? How important is it that I do the project I'm working on? The boss was angry to have been used in this way. The cow-orker was gone on Friday.