CB HI is basically right your rights. The driver has the obligation to put you in the position you were in before the crash.

Also, this is really chump change to an insurance company - it's easy for 5 mph parking lot crash to cause $2,500 in damage to a car. The real dynamic here is that the adjuster needs some sort of documentation to justify the payout. So that when the company does an annual file review/audit, he can justify why he paid out $2,500. Basically, he just needs some sort of documentation showing that this was the cost so he can put it in the file. No one is going to pore over the document and try to ding you because there's no proof that your existing spokes were double-butted. They just need some sort of paper for the file that plausibly justifies the cost.

That's the same thing that was going on with CB's Geico case. He calls the insurance company and says that Driver damaged his bike. They open a file and this is the first thing they write in it. They call Driver and he says it was the restaurant's fault. So this is added to the file. Obviously, if they paid out money without doing anything, this would be questionable in the audit. So they go out to check on Driver's story - not so much because they want to screw the restaurant, but because they need justification for the audit. So they measure and it shows Driver is at fault - this is added to the file, along with documentation for a $500 repair. They pay out $500, the file is complete, and they go on to the next case.