Jeez Cosworth211 you are not even a fully qualified pilot yet but you are starting to sound very high and mighty already so no doubt you'll be fine when you qualify!
(However the impression I get is that the supervisors and reps have no comprehension of the potential disaster that looms when ID requirements are waived, or load sheets are massively underestimated.)
You are a condescending twit if you really believe that statement!! Very few pilots have ever been on check-in yet there are a lot who pronounce words of wisdom on the subject as if they know everything, whilst clearly demonstrating they do not. Do you think that Reps and Suoervisors are just pulled off the street every morning?
2 people travelling together on a booking are fine to combine their baggage allowance, and allowing someone to 'use' a part of someone else's allowance has been standrd practice for many years as a way of resolving excess issues. There is no 'security' issue as both parties present their bags and answer the security questions for their own bags, it is simply a 'pooling' of the allowances.
Re travel documents, I would expect the Supervisor to have several years more experience than our GF, and maybe she recognised the travel document as acceptable; had dealt with the issue before and knew it was acceptable at the airport of arrival. In view of how much trouble the Immigration services can cause for an airline if they do not comply with the regs it is highly unlikely that a Supervisor would take risks.
Enough other people have commented on the bag weight issue, but what I cannot understand is why your GF had to refer the issue in the first place? If she cannot explain the regs to a passenger and persuade them to shed 3 kgs from their baggage to bring it in weight then she isn't doing a very competent job. I know other c-in agents who are quite capable of dealing with these situations on their own.