Thank you and nosebear for the clarification! Now I understand better why some of my colleagues (like my boss, older) use "Du" and some don't. I'll stick to not using it, there are enough grammatic pitfalls elsewhere in the German language (not that French is any easier for foreigners, I'm sure).
I love and hate German for this; it's a language whose formal pitfalls and vagaries seem almost designed to sort people into highly-refined strata of education.
It must be so cool to see all of them "from the top" (i.e. someone who has been natively-and-highly educated, immersed in the language for their whole life); but it's from the outside it's like a fancy club that you just can't seem to get into :)
