Update!
I've had a chat with the person responsible for contracts and personnel in my workplace. She is not from HR but is the closest I could get at short notice.
She confirmed we are not only allowed but also expected to provide reference letters, both for students and employees.
She confirmed that HR would refuse to do this, and that if pushed, would only confirm role and dates of employment
She agreed it was a difficult situation because "we are always told not to lie"
Her first suggestion (unprompted) was to tick 'no' and explain why.
She recalled how pissed off she was that a colleague from another department did not warn her about a bad employee
We talked a bit more about how different her new rol is, whether I thought she would perform well, and speculated if some of her bad 'traits' might be carried over to the new position.
I made clear I did not intent to jeopardise her new job, and
We finally agreed on ticking Yes to avoid any problems, but also adding a "provided the role was suitable" or similar
We also said the wording of the form should just be "is the candidate employable?" (Instead of would YOU re-employ them)