1000% false.
Facts. https://www.fordtremor.com/threads/the-tremor-towing-table.4262/
I own several F250 and F350 7.3 work trucks that occasionally tow 10k lbs, equipment trailer + mini excavator or loader (use mostly F450 and F550 6.7's for this usually). I tow a 20k lb toy hauler with my 6.7 Tremor. My 6.7 tows 20k lbs 100 times better than our 7.3's tow 10k lbs.
As you allude, if you're regularly towing 20K# you're not choosing either F250-350 to do it. Especially if you're towing 20K# of equipment that costs some multiple of the truck. The F450-550 is the right choice there.
And, sure, the more power the motor in the truck has, the less you have to press the pedal as you hang more weight off the back. But if that's anything more than a vanity metric you might want to do some light leg exercises.
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