There are four separate issues that are getting conflated in the PADI information:
The difference physical depth that occurs between fresh versus salt water,
The residual nitrogen that occurs when you travel from a low altitude to a higher altitude,
The differences in atmospheric pressure at sea level and at altitude, and it's effects on deco calculations, and
The absolute pressure of the gas mix being used - it's Maximum Operating Depth (MOD) and Equivalent Air Depth (END).
1. The difference between fresh and salt water is mostly a moot issue. Some high altitude dive capable computers adjust the depth display to reflect the greater actual depth that occurs at a given pressure in fresh water due to its lower density than salt water, but the computer itself will still be crunching the numbers for the deco calculations based on the water pressure, and the atmospheric pressure, not the physical distance below the surface. If you're diving tables with a regular depth gauge, that gauge is reading pressure in feet sea water. It's your max depth that you adjust on the table to correct for the higher altitude and the few feet difference in physical distance between seas water and fresh water depth is a non issue, as it's already accounted for in the altitude table correction.
2. Residual nitrogen can be an issue depending on where you came from prior to starting the dive.
For example, back in the day I slipped my boat in a 150 ft deep lake at 4575 ft MSL altitude. If I drove up from Rapid City (3200 ft MSL) and made a dive, I'd be a group "C" diver on arrival due to the "residual" nitrogen from 1,575 ft my ascent up the hill from a lower altitude to a higher altitude. I'd have to take that into account in the deco plan for the first dive of the weekend. On the other hand if I drove to the lake from home in Lead SD at an altitude of 5,400 ft MSL, I didn't have to worry about it, as I was on gassing at the lake already due to the lower altitude I had descended to.
Based on 1 & 2, a caution with using a dive computer at altitude is needed as the computer has to account for the lower atmospheric pressure and thus "correct" the depth used in its calculations accordingly. And ideally, it will ask you to either input the elevation of where you came from, or ask you to turn it on before you leave home so it can address any RNT issues. If not, you need to dive it conservatively and be aware that you've got some RNT that it's not taking into account.
3. The altitude at the lake also meant that one atmosphere was a little less than 33 feet of fresh water. Given the lower atmospheric pressure at the surface at 4,575' MSL, at a depth of 110 fsw depth at 4575' MSL, the pressure isn't equal to 4.33 ATM, it's actual equal to 5.0 ATM, and the corrected depth used for decompression calculation purposes is consequently deeper. In this case the 110 fsw depth is corrected for altitude to 132 fsw for deco calculation purposes and that's the depth I'd use for decompression planning.
The stops depths also varied a bit as a 10' stop would be corrected to 8' and a 20' stop would be corrected to 16' to adjust for the lower atmospheric pressure at the surface to which I would ultimately surface.
While the decompression schedule had to be based on the altitude corrected depth of 132 ft, I could still use the actual 110 ft depth of the dive for gas planning purposes as that was the actual pressure I was at, and the volume of gas in each breath is based on actual pressure and depth, not altitude corrected depth.
4. Similarly, the MOD and END of the mix were still the same as if I were diving at sea level. If I were diving 32% at the pressure depth of 110 ft, the PPO2 was still 1.38, not the 1.6 I'd have a pressure depth of 132 ft, because it's the absolute pressure of the oxygen and nitrogen that have the effects on my body. Which means I'd have the same amount of narcosis on a 110' dive in a lake at 4,575' MSL as I'd have on a 110' ft dive at sea level.
In summary, the only things that are different in a high altitude dive area a) a few feet difference in actual physical depth at the same pressure, and b) deco schedules and stop depths based on the lower atmospheric pressure at the surface. The MOD and END of the mixes used are exactly the same at the same depths measured on a gauge calibrated in feet sea water.
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That's apparently too much for the folks that develop PADI instructional materials to grasp.