The european car industry dropped live axles on any car in the 70's with the demise of, you guessed it, the rear wheel drive Ford Escort.
I think the term anti-sway refers to the tendency of the rear axle to be only loosely attached to the car via a pair of cart springs. The bar would cause a significant reduction in lateral movement or 'sway'.
With independant suspension the bar has more of an effect in reducing body roll, or lean in corners (turns). This explains 'our' term - anti-roll bar which I think is a better description of what it does to the vehicles dynamics.
This of course, is simply my opinion and not based on fact or any real depth of knowledge!
A6 2.7t 01my 6spd Avant 51k miles
A4 2.0FSi SE 03.8 22k miles - Wifey's new one - the golf was not luxurious enough.
Golf Tdi 03.08 130pd, 6spd, 19k miles - Sold 8th November 2006 - gone to Coventry!
A6 2.8q 98.11 115K miles - sold 20th Feb 2006
100 2.8q 92.1 147k miles - Sold 6th July 2004 - its new home is Edinburgh
A4 1.6 97.8 99k miles - Sold 12th Feb 03
VW Golf Gti 86 22k miles 2.0 Oettinger 190bhp, lowered, lightened and quick and sold 23/03/08.