No, what happens at higher altitudes (less air) is the AFR becomes too rich, so the fuel mixture needs to be leaned out.
This "1.5 turn out" business as a general observation is simply a rough bench setting, if it were a permanent or one size fits all, then they would have done away with the parts & adjustment altogether and use a fixed orifice size. Think about it. They are actually VERY precise in their adjustment. You can see this in carbureted automotive engines by observing the AFR when making an idle mixture adjustment, just a 1/4 turn of will move the air fuel ratio a couple points.
It is also temperature dependent to some degree (heh) 2 stroke lawnmowers are different in that they should not run smooth at idle. Slightly ragged at idle, though settle in to the characteristic "LawnBoy hum" under load in thick heavy turf. Make sure there are no vacuum leaks and float height is correct or it will never run right. With the engine warmed up, turn the altitude screw in slowly clockwise. There should be a noticeable, definite point where the engine speed increases. This is the "spot" where it starts to be too lean (even at idle). Back it off slightly, just a smidge. Remember, these are precision cut needle screws. 1/4 turn out from this "spot" would probably leave it a little too rich, though safe for a wide range of temperatures i.e. it won't grenade the engine. I listen to the motor in operation and make a slight adjustment now and then through the season, on earlier models it only takes a split second, the screw is accessible by hand, no jiggery-pokery required. In the fall, during cold weather at the last mow(s) of the season it can need a pretty significant re-adjustment.
The power difference is very noticeable when they are dialed in "by the book".
"Slightly rich" is good and what the engines want, but this is still quite a bit leaner than many might think. "Slightly" is the operative word here, "1.5 turns out" is likely way, way off and an overrich condition leads to fouled plugs and excessive carbon buildup.
Another factor to consider is the 2 stroke oil to fuel mix. Adding more oil to the fuel than specified makes the air fuel mix leaner, not richer. Less fuel = leaner AFR. If you're using the modern synthetic 2-stroke oil mixes at 50-1 or more the engine will want a leaner setting.