Definitely NOT true if you take the above mentioned steps and just use a little common sense. Lots of the big browns in the Smokies have been caught multiple times by multiple anglers. Those big fish are pretty easy to identify most of the time. Also, you don't see dead fish lying all over the stream bottom and based on the quality of anglers fishing Smokies streams and resulting numbers of fish caught, if there was a high mortality rate you would see dead fish around.
Of course, things like mortality rate go up significantly when the fish are already experiencing environmental stresses. I generally see dead fish on the Caney in late summer when the dissolved oxygen becomes an issue. Keeping those fish out of the water or fighting them too long is a much bigger problem than carefully holding them for a few seconds. I've seen 12 inch rainbows fought for over 5 minutes in late summer on the Caney and that should never happen.