The stock timing gear on the cam has fiber teeth, so they could have broke off, or the the gear is just spinning as mentioned above. The cam gear is a press fit on the cam (no retaining bolt), and with all the Dieseling, it could have kicked back a few times really hard and is now just spinning the gears.
They have no choice but to pull the front off the engine. The camshaft will have to be removed for a replacement gear to be put back on. If they try to install it in the engine, they can push the cam right out of the back of the block. The correct way to install the cam gear is to heat up the gear to 200 or 300 degrees and freeze the camshaft. Make sure the retainer plate is on the cam ( the plate holds the cam in place once in the block) and drop the gear on the cam and tap it in place as quickly as you can before it cools. I have read that if you just press the gear on cold, you just open up the aluminum gear to the camshaft diameter. It will hold for a while but could come loose. By heating the gear, you expand it out slightly and once it cools, it returns to it original size which it very tight on the cam.
As for the dieseling, rebuild the carburetor and set the idle slower. If yours has a idle solenoid ( electrical solenoid about 1.5" diameter) make sure its working. Try shutting the truck off in gear, that will keep it from running on.
Good luck with your truck and keep us posted on the repairs. Joe