You are not likely to get the warranty company to change their stance.
Can you get the technician to give you his opinion in writing? If so, an approach could be to authorize the work, keep all the old parts, then file a small claims action against the warranty company. With the old parts in hand, obtain the opinion of other experts, such as tech school instructors and other technicians.
In court provide the technicians letter as evidence along with the parts in question.
There is a good chance that the warranty company will not show in court, and even if they do, most small claims judges arn't too happy with extended warranty companies.
To keep the clutch parts, you may need to pay a core charge, but you should get it all back plus your filing fee if you win the jundgment.
I'm trying to picture how a worn or burned clutch is going to cause synchros to wear. Maybe they are trying to claim the clutch wear is an indication on how you drive the car.
Unless there is something I don't see, I don't understand their reason for not honoring the claim.