But the thing is the judge gave them exactly that option and Ulbricht's lawyer inexplicably declined to take it - see page 22 onwards.

So either a) Ulbright can't prove he owns the server (in which case he can't very well claim privacy rights in something that's not his property to start with), or b) he is not willing to, even though doing so might keep most of the evidence out of trial. Maybe that's because of some super-clever legal tactic they plan to unveil at appeal (although this seems very unlikely, as this is such a basic procedural issue) or maybe it's for some extrajudicial reason, like because it would reveal the identity of some partner in crime who would then seek terrible revenge. Or any other number of other possibilities.

Shouldn't the government's claim that the server was owned by Ulbright effectively concede the point?

I don't know, but I think Ulbricht would need to concede that explictly. I don't feel like digging through all the filings to try and figure out his counsel's strategy at this hour, though.