The problem is that its just impossible for her new employer to know if she's genuinely sick or just messing them about. Whether this is going to be a genuine one-off with awful timing, or whether she's about to be another employee who is off every couple of weeks 'ill' with something and is totally unreliable. Working as a TA in a school, that's a huge problem.
She's got no history with them at all, so they just can't know. It's great to say they should just believe her, but that's not actually where people-managing leaves you. People lie. They just do. And they lie about being sick - a lot. Look how often 'just ring in sick' is used on here.
The sad reality is that there are people who would take a job, then blow off the 1st day just because they don't feel like it that day, or something else has come up, or they got the date wrong or, or, or... They just don't see an issue with it
I've had staff accept a job, get right to the end of their several week notice period and be due to start, ring in sick day one - and only then ring in on day two to tell us that they weren't sick at all on day one, but at an interview for another role which they'd applied for after accepting our role and have been offered that job and so they aren't starting at all, tatty bye!
Missing day one with a 'self-certified minor illness', is a huge red-flag for management and HR, and it does and will get remembered. Yes, if she's still there with an impeccable record years later, it'll become an in-joke, but it'll mark her card with a cloud for a long time before then.
Op, if you're absolutely not fit to be in, ring in as early as you possibly can, offer to snap shot the script or the prescription and send it (it offer some proof of a real issue) and apologise profoundly. I wouldn't go as far as suggesting tena-lady (that's a bit much!) but if you can stand, move and drive, make the effort.