I will share some personal experience, mostly from my job. I am a land surveyor and either me or my co-workers have been stuck numerous times. We have had 4 wheel drive trucks, but as a rule they have been 2 wheel drive. I once had to pull the surveyor crew off and icy road. It was snowy and the snow had packed down to where it was icy. It was a fairly narrow road and they just barely pulled off, not even in the ditch. It was flat ground and the thing wouldn't move. If it was 4 wheel drive, it would have driven away with no problems. All the company trucks I've pulled out were 2 wheel drive.
My current truck I got it stuck in the mud once, and it was very stuck, it took a back hoe to pull it out. Like you say, mud and a heavy truck don't work well.
One of the best 4x4 vehicles we had was a Bronco II. It had crap street tires that were mostly wore out, but it was light, turned tight, and would walk out of places that left you shaking your head.
I'll just say my current truck, a 2004 Dodge 3/4 ton with a Cummins does as well as anything in the snow I've driven, but I'm afraid to go near the mud again.
The advice to drive a 4x4 like a 2 wheel drive isn't that bad of advice except to have the thing in 4 wheel drive already, and if you see a place that is doubtfull, you will probably get stuck.
I've been stuck to many times to think any vehicle is invincible. I've seen a D8 dozer stuck once, but that's another story.