The statement was not for LED's in general. (It's really the resistors that cause the heat.) The quote was specifically for the 'double-double density LEDTape' I sell through Modeler's Brand.
In that particular case, the LED's are crammed so close, the resistors get hot and the clear gel coat insulates that heat, internalizing it more than anything else.
In a recent test, I had a 1ft strip enclosed in a very snug space (1" x 1" x 1'). Between 48-72 hrs, 1/3 of the LED's suffered heat death. Some were totally out, most were sharply reduced in brightness to one degree or another. There was no damage to the plastic surface the Double-D was attached too. A computer case is wide open for heat dissipation so it's not as big a deal.
I have 14 feet of Smooth LEDTape in my machine which runs 24/7 for weeks on end. I would not do the same with the Double-D. Not for that long a time. The stuff gets too hot for computers cases generally. The normal LEDTape, at 3 LED's/Inch instead of six/inch runs cool for days on end.