It turns out that Smart Projects had trademarked the Arduino brand in Italy in December 2008, before Arduino LLC got around to filing in April 2009 in the USA.
So... what's to discuss. I don't think there's a law against being a complete asshole, so smart projects wins.
You don't "trademark" things -- you register a trademark. Registration is not strictly necessary in most jurisdictions -- as long as you are actively using the branding, it is automatically considered your trademark. Order of registration only matters if you're talking about two commercial entities independently coming up with the same brand. Here we have two entities with an existing contractual relationship. Smart Projects therefore was not ignorant of the informal body that later became Arduino LLC. Who initiated the contract and who came up with the name? What did the original contract say about the name? Clearly the initial contracts were poorly drafted, or there would be a clear answer, and we wouldn't be having this conversation!!
Well I learned something today. I guess I should have assumed that lawyers would make the problem as difficult to resolve as possible.