I think that we are all saying the same thing;
The pilot had to meet the renewal requirements legally. i.e. They had to have a valid medical etc when completing the flights claimed (except the dual flight). However, they do not need to hold a valid medical at the time the licence is signed.
eg Flying required completed During January. Medical expires in February, pilot completed dual flight in March and approaches Examiner in April to sign certificate that expires in May.
The pilot has demonstrated that they have legally met the requirements for the examiner to sign the licence page and the examiner has no legal basis for not signing the page.
Of course the pilot can not exercise the privileges until they have a medical but that could be their next port of call.
The whole thing gets messy when the pilot has completed the requirements legally but has say in the above example some solo flights during March with no medical. The pilot has met the requirements for the licence to be signed. The pilot has also made some illegal flights. Legally the examiner is required to sign the page but there is also the separate fact that the pilot has flown illegally which the CAA have issued guidance on.
Regards,
DFC