I can tell you where it was being taught: USN Carrier OPS.
As far as putting flaps down before gear, I think that is a huge mistake, especially in a Mooney. Whether abeam or at the FAF, you should do three things in order: Prop, Gear, Flaps (first notch), in fairly rapid succession. Building that habit will always keep you safest and results in slowing the airplane down enough for each of the next steps.
After my dad had a gear-up landing, his insurance insisted I fly with him on a permanent basis. I noticed that since the C-210 had a higher flap speed (first notch) than gear speed, he would operate the flaps first, then not be consistent about what he did next; either Prop, Gear, or second notch of Flaps. Even with his 5000 hours, the problem is that any distraction might throw off your habit pattern when you do not have a rock-solid pattern drilled into your brain. That is why I insist my student always use that order, especially in Mooneys.