About the use of the word "reduce", I agree with you in that you don't "reduce" VAT. But you're german man, I'm portuguese, I haven't a clue about bdbdbd's nationality (tokelau doesn't really fly), and we're trying to communicate in english... cause that's the best we can do.
I mean, technically, I know VAT is not "reduzido" in portuguese, it's "abatido". But I'm guessing you wouldn't know that, just as much as I don't know any german at all. And I really don't know how I'd put that in english, any better than "reduce". And since you haven't proposed an alternate english word in your 2 posts complaining about the word "reduce", I'd go as far as saying you probably don't know the technical term in english either (not that you should).
This isn't about being right or wrong, it's about making an honest effort to understand each other's meaning cross languages (we're european, not americans, we should know a bit more about that). We're all talking about the same thing (bdbdbd already said as much), complaining about terminology in a language that's not our own.
About the rest of your post, as I said, I wouldn't know either way. I'm not doubting you. Actually, I'd expect it to be without VAT, same as you do, as that's the default for business-to-business around here, even for unit purchases of products unrelated to one's core business (like the office supplies you mentioned). I have seen some prices like these quoted with VAT, however.