Back in the good old Bank of ****s, I was always on a "stage 2" attendance management thing, due to ongoing health issues, and it was quite interesting the logic of the thing. Stuff like a single day's absence being considered worse than a 3-day absence- so you haul yourself back to work as fast as possible, then find it causes you problems.
Every so often it escalated, and I'd have a conversation with a HR bod or manager that went like this:
"You're off quite a lot aren't you"
"Yes, I'm basically human wreckage"
"We'd prefer if you weren't"
"So would I!"
Highlight was being off for 10 weeks, returning to work for 2 days, basically collapsing then being off for another 2 weeks- did they say "Thanks for trying?" No they said "That's 2 seperate absences, much worse than one longer one" I'd have been better not bothering.
Eventually they would ask to speak to my doctor, and my doctor would get furious, call them names for a bit then charge them for the privilege. Then that'd reset it but next time I was off ill, off we went again.
Attendance management and disciplinary are usually very different, but 3 days in a year is trivial- it's reasonable for them to ask if there's something going on but not to treat her like she's done anything wrong.