AC compressor ground

Does the AC compressor ground wire have to be grounded to the compressor housing or can it be run to the frame or battery? Thanks

 

I'd keep it in the OEM position, which should be here. Note this user was having issues because someone installed a fastener that was too long and its bracket wasn't sitting tight. https://www.tundras.com/threads/a-c-blinking-light-over-pressurized-bad-ground.110897/

I'd be confident grounding it to the engine block, and don't see an advantage of grounding to chassis (since block is grounded to chassis) or the battery (since battery is grounded to chassis).