The Boss is leaving himself wide open to a legal proceedings.
There must be a procedure (written) in any workplace to govern what is acceptable behaviour and what is seen to be the required level of efficiency.
If this girl is being let go because she is inefficient he has to be able to back up that fact by having details of the training she received to attain efficiency, remedial training put in place to rectify any shortcomings following the discovery that she was not effective. At all stages the employee must be advised that her performance is not acceptable. Verbaly and followed up in writing as the case becomes more serious.
I have had to let staff go who had poor attendance. They weren't sacked for their sick record they were sacked for being inefficient.
It takes a lot of time to go throught the process and an employer has to prove that everything possible was done to try and rectify the problem.
Your boss is cutting a sick to beat himself with. May be advisable to have a quiet word if they are open to advice.
I thought this was the situation. I will do that, i think he needs to be told. And i may even put it in writing aswell.