Since Jun is not present in Halo: First strike, it can be assumed that he died transporting Halsey to Castle base.
Also, in the defiant video, if you look in the distance you can see another spartan body that has the same helmet as the near one. IMO they just copy and pasted Juns body for that video because he had the same armor color as the S-IIs.
Also, S-IIs did not all wear the same armor pieces. While they all received the same basic suit to start off (because ONI required clean cut iterations of the armor), Halsey's journal tells us that they all received customized pieces to fit their needs over the years.
Also, I feel that noble teams rainbow colored suits aren't exactly canonical, they were simply colored for the sake of gameplay, so they would be easier to tell apart.
I would have preferred they all be olive green. They would feel much more like a professional unit, not a bunch of scrubs.
[Edited on 08.09.2011 8:06 PM PDT]