Although sometimes you can get a bad tank of gas - See if they can hook up a real-time data acquisition logger and see what your sensors are telling the ECM. Pinging can occur during hard acceleration - which is normal - but excessive pinging is not a good thing.
I would have them double check the sensors - especially the knock sensor, which supposed to retard the timing if pinging occurs, and that the VVT actuator is functioning properly. Some people have had problems with VVT actuator and OCV (oil control valve) although - these going bad on a Corolla are remote.
Excessive carbon build-up inside the combustion chamber can cause excessive pinging - creates a hot spot with will prematurely light off. Rebuilt a Honda motor that had carbon deposits on the piston face and next to the valves that cause excessive pinging - eventually damaging some bearings and scoring of the piston bore (engine pulled from a donor car - unknown maintenance).
You also mentioned a drive shaft and rear axles - car is FWD doesn't have a drive shaft or rear axles. I hope you meant the input or output shaft bearings and front driveaxles.
Car should run fine on the 87 octane juice - with prices as they are, you should not have to pay more at the pump because these guys cannot figure it out. You can try a can of fuel injector / intake cleaner with a tank of gas to see if that does anything. They may have to use a borescope or pull the head off to check for carbon / foreign material build up. Have them correct this while it is under warranty - you should not have to accept this band-aid fix (the use of 91 octane).
Good Luck.
I have a 2002 Corolla S 5-speed that pings regardless of what brand or grade of g**** is used. (It does ping more with 87 octane). It has 43,000 miles. I took it to the dealer and they confirmed that it does ping excessively. They checked everything and all is within spec. They could only recommend that I use 91 octane gas and try different brands.
THank you for the response.