The background: Having been previously in two mobile phone shops near first a Nokia cable, then a BlackBerry Cable, me my third attempt resulted in a large electronics market and a no-name product that Verte cables came on eBay (the seller gave explicitly that it was up for the ATV). Has been tested with two ATV equipment, both 2nd generation, on two computers (Win 7, OS X) with FireCore's aTV Flash. Not one of the four cable worked. The regular Restore via iTunes failed.
So I ended up in this Amazon product. Delivery arrived very quickly, was the bargain price lower than in the previous four cables. And it did what it should. Have again tested with two AppleTVs each under Win7 OS X and the cable - is working properly!
Out of interest, I then also tested the cable to a BlackBerry and a Nokia phone, again no problems.