The big guy who works in that excellent museum hands out incorrect "facts" about 1/3 of the time, from the various TotG episodes I've seen him in.  You *really* have to take stuff on TV, even from so-called "experts", with a grain of salt.

When the M16 was first issued to standard troops for Vietnam use in 1965 (they were in use by ARVN and US advisors on a limited basis, as well as by a SEAL team, before this), the ammo was issued in boxes.  SOP was to empty the ammo out of the boxes onto a poncho and proceed to load mags.  Occasionally, GIs would load one-too-many rounds in one of their mags.  Most 20-round AR mags can hold 21 rounds if you force the last one in, but if you do, they won't feed.

In addition, if you take the spring/follower assembly out of a 20-round mag and turn the spring 180 degrees on the follower, you can still reassemble the mag, but if you put more than about 18 rounds into the mag, the follower will bind at the bottom of the mag body and the ammo won't feed.  These issues started the practice of loading only 18 rounds (or even less in some units) in 20-round mags.

Both of these simple issues caused problems for GIs in Vietnam, along with the other, more serious problems being encountered with the M16 early in the war.  Both problems were, in large part, corrected by '68.  By then, ammo was being issued in bandoleers on stripper clips, removing the need to count individiual rounds, and GIs were being trained not to remove the follower from the spring and the proper relationship of the spring to the follower.  Once ammo was issued on stripper clips, GIs were (re)trained to use 2 full stripper clips of ammo per 20-round mag.

Unfortunately, there were many soldiers from early in the war who went back home to the US to train new soldiers, and among the things that those soldiers were often taught was the 18-in-20 "rule."  And due to the problems with the M16 and the general distrust of the military at the time, these words from combat veterans carried a lot of weight with those soldiers, even though they no longer fit with the current situation.

The problem of myths and inaccuracies being passed along continues to this day...

-Troy