my understanding that it is part of the FTO's job to make sure their student (after all a paying customer) meets all requirments for license issue.
Not true.
The information is in the document entitled "Guidance for Applicants"
It rests with the student and of course the examiner who tested said applicant.
Any FTO which takes the responsibility of this into their hands is failing their student by not making them take the responsibility for complying with regulations. The approach of having the "FTO" being responsible actually represents worse customer service because at Commercial level they should be instilling that the word "Commercial Pilot" means that said Pilot only is responsible for ensuring compliance.
If said student didn't check (overseen by FTO agreed) then they've been failed the student totally in instilling the legal responsibilities of a commercial pilot much earlier in their CPL training.
During Commercial training the emphasis should be Commercial pilot first, paying customer second. A good school will balance it this way, ensuring that the latter is not totally ignored. Any other attitude will eventually lead to an attitude of not taking responsibility, and possible a hazardous approach, as pilots shy away from their legal responsibilities due to poor primary training in this area (Primacy).