I don't know other than what was provided to her in a simple Q&A document. She's technically in a grant funded training program. Her stipend is considered a fellowship and not compensation. The terms of the funding grant prohibit her from being classified as an employee by the organization that actually issues her paycheck.
Some people in her program use that fellowship to pay tuition for a concurrent graduate degree program. She has other funding sources to cover the tuition, so she's able to receive the fellowship funding as salary.
As a trainee, she is exempt from FICA, Social Security and Medicare taxes. That's pretty clear in the reading I've done.
Oddly, her state and local taxes are withheld from her paycheck.
I think we're okay on the divorce issue... unless she's secretly plotting against me, in which case I've got bigger problems to worry about.