Hahaha, I also just realized this reading through - Des is very laid back about Alex poking through his memories. I guess that's a side-effect from going through Altair and Ezio's memories, that his personal memories aren't exactly the sacred be-all and end-all of privacy to him. Plus he still thinks Alex is one of his ancestors at that point.

I can also see Shaun and Rebecca wanting to know who Alex is, personality wise, since Des is now sharing head-space with him. And Des is like
D: ..... *shrug* he's... Alex.
S: *dryly* Yes, that's very helpful there.
Becca: Oh c'mon Desmond, what's he like, I mean, all we have is some badly shot cellphone footage of him being a one-man-army and the media going on about how he's evil incarnate.
D: *rolls eyes* He's not evil, don't worry. *thinks about it some* Alex is.... focused? Impatient?
Alex: Hey, I'm not impatient!
D: *snerk* Okay, okay fine you're not impatient. You just don't like to wait.
Dana: Yep, that sounds like Alex.
Alex: ...er.
D: *snicker*