The military press/strict press was a lift that was done at the olympics. These guys were pushing 200kg's, and they had to have their legs locked.
Doesn't matter what people do or what people call things, the military press is done standing, with legs locked. It's not made up gym rules, it was a sanctioned olympic lift.
If you want to military press, stand up, knees locked, and don't bend your back too far. If you feel you are straining your back, stop the exercises and/or drop the weight. Work on your core strength and lower back strength.
If you just want to overhead press, then doing whatever way you want. Bent knees, split legs, sitting down, upside down....who cares.