As stated above, a big knife is not always required but it does make some tasks easier. We are talking about emergency survival where having over-built, over-engineerd equipment is desired, tempered by weight considerations. Building a log cabin with a Leatherman tool is a Masters thesis (or a stunt)not a survival strategy.
I don't like digging with a knife but I can turn a piece of dead wood into a shovel a lot faster with a big chopper.
It is also faster and easier to split out fire wood to get to the dry center after a 4 day rain.
In snow country a large blade can be useful as a snow knife for shelter building.
Although we don't cut live trees to build shelters much any more, in a true emergency one can turn a spruce tree into a good shelter in minutes with a big knife.
Granted a hatchet will do as well but I find a large knife easier to carry on the belt and fits better in a small survival kit. By "large" I am referring to a range from the 7" bladed K-Bar to a 10" bowie, with a weight range of 16-24 ozs sheath included. To me anything smaller/lighter is a small knife. Anything bigger is a machete or bolo.
You asked for true stories. I have never been in what I consider a true live or die survival situation but there has been a time or two when using a big knife to help get a fire going in wet or extreme cold has probably kept me out of trouble.
Leo