How do you program a 2007 Mazda 3 keyless remote?

I found this identical information on both an "authoritative" Mazda site and on 2 mazda enthusiast forums:

Programming a Spare Remote for Mazda3

Step 1: Open driver side door and leave open.

Step 2: Lock and Unlock the drivers door using the power door lock switch on the door

Step 3: Insert key into the ignition.

Step 4: Turn Key to ON position and return to Lock (off) position. Do this 3 times within 10 seconds. LEAVE key in the ignition in Lock (off) position.

Step 5: Close and open drivers door 3 times ending with door in the open position.

Step 6: ECU should respond by locking and unlocking the doors once.

Step 7: Press any button on remote #1 twice. ECU responds by locking and unlocking the car doors.

Step 8: Additional remotes, repeat Step 7 for up to 3 remotes total.

Step 9: Remove the key from the ignition and the ECU will respond a final time with a series (about 4) of door locks and unlocks. You're done!