@w3c once overheard a tour guide at CERN "you see this plate? This is where the world wide web was invented. Do you know what this means? The world wide web - the INTERNET - was invented here"

That said, I don't think pedantry helps us anything here. www is colloquially just internet in 90ies English, so include the Wikipedia articles on the t-shirts or don't bother. The guide was tiptoeing the line of "technically correct while deliberately misleading" and slipped into "actually wrong".