Pretty sure its not supposed to count keys sent to other players.

Golbez wipes himself out with magic

Jump down transition where one should not be.

Goose getting dizzy

Sending Two keys down the well.

Torch keys are not counted in the total

Thieves town edge transition softlock

And this is why counting keys for other players is bad.

Final Fantasy 4 Free Enterprise - 2v2 Practice with Komura