Excuses? Very strange comment / way to put it, I'm just stating what I've seen without having to google it on YouTube. If anything your post comes across as defensive, but again, this is a quantitative / pratical discussion not an emotional one.....
I'd disagree, most Gas / Petrol rigs have much different powerbands.....always exceptions (as all your examples seem to be), but generally gas has more HP at higher RPM, both of which are good for sand based on my experience and observations.
Gas rigs generally have a higher HP / weight and broader powerband. For most rigs, diesels have lower HP vs gas so I'd disagree there is not a difference in power....for full size trucks they are close, but for many other vehicle types Gas engines are generally more 'powerful' across a broader RPM. Using the Jeep gas vs diesel:
Diesel 3.0; 260 hp @ 3600 RPM (effective range 1300 to 3600); spread of 2300
Gas 3.6; 285 hp @ 6400 RPM (effective range 2000 to 6400); spread of 4400
Doesn't get much different than that, using the example you gave, that's what, ~85%+ more RPM range, which can be important in mud and sand.
Same story for full size rigs, but more extreme, look at Ford:
Diesel 6.7; 475 hp @ 2600 RPM (range 1000 to 2600); spread of 1600
Gas 7.3; 455 hp @ 5500 RPM (range 2000 to 5500); spread of 3500
More than 2x.....