This is true. I usually stretch my strings after putting new ones on to try to minimize the effect of stretching, though. Helps stay in tune when you bend a lot. Remove old strings, put new strings on, tune new strings up to pitch, stretch them by pulling them a few inches off the fretboard and moving them side to side like you're doing a bend, marvel at how flat your just-tuned strings now are, and then retune to pitch.
For maximum tuning stability, I also put locking tuners on my guitars and lubricate all of the parts where the string touches. This includes the nut, the saddle, and any string trees.
I use a humorous product called Big Bends Nut Sauce but I've heard graphite from a pencil works as well.
