Why exactly? For a 1,000 lb load? Are you serious?
People think they need a big stupid ¾ ton to go get mulch at home depot once a year. Get real man.
¾ ton trucks are a headache to own, especially diesels. A Tundra will move 1,000 lbs around without issue. The original post is alluding to something that some uninformed told them at an auto repair shop which is absurd to begin with. These are million mile trucks that are underrated for capacity.
It will move it - sure, but it's (potentially) outside of it's design intent. A stock Tundra has a payload capacity of ~1600 lbs (give or take), 2 dudes + gear is 500 lbs easy. Add in 100 lbs of offroad goodies, you can see the trucks realistically are rated for ~1000 lbs in the bed....that is Toyota engineer constraints, not the auto shop guy that gave the OP good sound advice, it may not be the frame per-se, but it's certainly a risk.
3/4t's make a bunch of sense for the OP or anybody with a full size camper, especially if they plan on going offroad in challenging terrain.....much stronger running gear and frame than a Tundra and leaves a larger factor of safety, which is a good thing. Loaded down they get sim. MPG. I'd rather have an understressed vehicle than an overstressed one....
Driving to and from Home Depot is not best use case for a 3/4t, but if you have a huge travel trailer at home they need it since a 1/2t won't cut it....many guys are in the camp, but of course many guys don't and would probably be better served with a lighter duty truck like a Tundra or a Camry.
I've kinda come to the realization that full size campers work better on 3/4t+ trucks, less stress, same MPG, better handling & ride when loaded down, within design limits, etc.