Not totally true. Iv had my Stratocaster since 1988 and have been replacing the strings just how you do (I take off all the strings at once). Maybe by theory your friend would be right, but it doubt it would make a difference. Espcially when it only takes seconds to take the strings off the guitar and put new ones on.

I have never heard of the neck warping because of such a reason. Actually the guitar neck is made in such a way that these kinds of small things wont affect it. But im not 100% positive about it... ;)