As I thought, in the 2009-onwards Corolla, the stock mounting bolts go in from the top, and have captive nuts at the bottom that are sandwiched between layers of the rear parcel shelf and bulkhead, and thus are NOT accessible from the bottom:
Left side speaker:

Right side speaker:

Closeup of bolt:

(Also note the grey bitumastic compound on the bolt shaft used to prevent loosening over time due to vibrations.)