So (in the link) you say that there are signed notes of the meeting in her personnel file.
a) whose signatures are on the report? - if it's the manager who wrote the report, that's fine. As BM says, they don't have to be signed by the person receiving the warning
b) have you looked at your organisation's disciplinary and grievance policy? That will lay out all the processes and make the steps very clear (I know ours does)
b) do you have a union?
c) if not, call ACAS for advice, their helpline is free and impartial
If she had a warning then the management would have kept an eye on her for six months to make sure there was no repeat.
I'm a bit unclear about why she was called into the office in the first place. You say it was an investigation about something else, then you say it was for supervision (and for people not working in a health/care setting, my understanding of supervision is a regular meeting to discuss work, how you're coping with certain cases, learning from incidents, etc.)