Thanks for your reply. That's what I was afraid of.
What was not immediately clear to me was that my iPod could not be upgraded (they mention this only at the very very end of their info. I searched the site, without success - I never found the link to "Identifying iPod models".
Apple doesn't mention that they sold many refurbished iPod Touch 2nd generation models with the 3rd generation software effectively making them a 3rd generation unit.
Anyway, this proves again that you should always check with an expert before buying.