"I'm fairly sure at some point in the past my school made the administrative decision to have fellows/Phd students slapped on to the existing staff payroll system and so that's just how it goes there. I wouldn't think the particulars would make a difference but it does serve to make me more uncomfortable about saying 'zero income' as I'm on payroll with a staff number."
For what it's worth, I wouldn't worry about this - I'm a USC and since I retired, I've been an research Fellow at a UK university which is a staff position but I get zero income and it's never been an issue.
Do you know that the US embassy in London has an IRS office where you can call and talk to a tax advisor. You can also go there. Check the embassy web page for their office hours.