Some readers on Jalopnik's site said that the cars actually weigh very similarly. So "lighter" is only perceived.

Well, that would explain the disappointing improvement in average fuel economy.

Is it really that common?

Mostly among the 40 and up crowd, I think. I'm not sure I know anyone younger than me who believed that (I'm 36).

I'm 28 and my primary inclination was to think that newer vehicles crumple while older cars do not, leading to more internal injuries for passengers of older vehicles and more vehicle damage of newer vehicles. However it appears that the older vehicles lose on both fronts.

I don't know and can't provide anything but anecdotal evidence, but I do get the sense that "they don't make 'em like they used to" (== those old cars were solid) is the prevailing belief when I talk to people my dad's age (50+).