bednobs and factor - you are both correct on this.
Dot is not the only person who believes that 'sacking someone' (your words - I prefer 'dismissal' - sacking is something you read about in The Sun, or worse) equates to 'redundancy'. It doesn't.
Competence, capability and redundancy are 3 different reasons of the possible fair reasons for dismissal - there are a few others. In this case an employer would dismiss on grounds of capability, because treborrobert is not capable of doing the job.
It may not be that straight-forward for the employer because in the short term it is perfectly reasonable that the employer should be expected to adapt the job to 'light duties' to allow an employee to recover from a medical problem. But there is no obligation that it has to continue indefinitely.
Absence is a separate issue. 6 weeks out of the last 12 months sounds a lot, but it depends how many occasions. 6 occasions each of one week long would be too many, especially if for different reasons (in my opinion - there is no fixed rule) - one occasion of a bad sickness of 6 weeks long should be regarded as more acceptable (as a one-off).