I agree with your concerns - Car owners today are held to ransome by garages. You just have to go to the garage and trust them to do the work an pay through the nose for it.
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If a cam belt change has been done properly you can usually tell the difference when you next drive the car as the engine sounds quieter and may even drive smoother..
On some cars because the cam belt cover is flimsy it is possible to ease the cam belt cover to one side revealing the belt, before the car is taken to the garage paint a blob of white correction fluid on the belt (the engine must be switched of off first of course) .Ask the garage to leave the old belt in the car when you come to collect it. the old belt should still bear the white mark thus proving it has been changed and taken from your car. keep the garage invoice for future proof should you have any trouble with the belt in the future (within specified service intervals).