It's true. I've never seen a shooter take more than about two or three seconds to change magazines when they had a magazine change as part of the drill, and a good shooter does it in less than a second. Some are good enough to where you barely detect the pause in the shots during aimed fire.
The Newtown shooter reportedly changed magazines frequently, leaving a trail of them, and changed them long before he needed to (he was leaving half-empty ones behind him). It's speculated that he did so because he was used to video games where the screen will flash "reload" long before a magazine is depleted.
In a situation where 30 rounds are aimed and fired, changing magazines once versus changing them five times (six rounders) is going to add about two to four seconds to the elapsed time (going from about 20 seconds to 22, 23, or 24 seconds total). Our murder rate was much worse when people were still using revolvers.
Our first school massacre was done with tomahawks and knifes, I think leaving only one survivor. Our worst school massacre was an inside job by the caretaker, done with explosives carefully placed over a sixth month period.