Queen mate

Not always true.
In this position,
1. I got the king stuck at a corner.
2. I got my king near to the enemy king.
Stalemate! (With Black to move)

A good rule of thumb is to stay a knights jump distance away from the king until the king is in the corner, that’s a stalemate.

This method is just awful. Nobody should bother to learn it. And anyone who teaches this to students is doing them a huge disservice.
One of the main problems is that this method leads you nowhere. If you have a rook instead of a queen, the method does not work. Another problem is that it is needlessly long and repetitive.
The example that JTorreslolz gave is a perfect example. Anyone with a functioning brain would play 1. Ke4 (bringing the king into the action). It is mate in 4. Instead, the dumb method is mate in 7. Also, if you replace the queen with a rook, 1. Ke4 is still the fastest mate while 1. Re6 is a pointless loss of a tempo.