That is a myth. ALL bullets alter trajectory when impacting media. The weight of the bullet causes easier fragmentation, as it simply isnt as dense as a 7.62 round. "Observed tumbling" is something people will occasionally see, when shooting paper-the bullet passed through it sideways, in what is called "keyholing". This is the result of the shooter having a poor grip, and anticipating recoil-in essence, you are putting a slight flid on the bullet when it leaves the muzzle, causing it to keyhole.
As to the tumbling bullet theory, I think that this was one of the "plastic gun" myths originating when Stoner introduced the platform. Most of the trouble issues with the M16 platform were found, and dealt with, within the first few years of production. Or the result of negligence on the shooters part. Having shot them in one style or another over the course of 20 years, I have never had one blow up, or get so fouled as to not work. Sure, I have had jams-show me a rifle that doesnt jam!. But, I can honestly say, a well built AR platform will provide years of service, with minimal effort required on your part.
FYI, there were recent studies done on how the military cleans their rifles, and premature replacement of parts. Anyone who has served, I am sure has expereinced the HOURS of cleaning the higher ups require. Armorers often would not take a rifle with ANY carbon on it at all. This is actually quite detrimental to the rifle. Wiping down the bolt carrier group, the chamber, and rodding the barrel, is all thats needed. 10 minutes, no more. A little carbon is fine-it doesnt cause jamming issues. Oh, and, of course, a little oil.