As far as I know, we have three elected moderators: gandalf3, iKlsR, and David. This begs the question, who are Gabe, Oded, Robert Cartaino, and however many others that I've missed? How are they moderators?
There are 490 moderator across all the SE sites. (so you are bound to see a diamond or two.)
Yet only the three BSE mods (gandalf3, iKlsR, and me) and SE employees will have diamonds attached to our name on this site.
The three users you linked to are employees of SE (and have mod+ abilities on every site.)
Oded is a dev at SE.
Robert Cartaino is a community manager (CM). CMs have more power then mods, they over see all the sites and come by when help is needed.
While I personally don't know Gabe, his profile says that he too is a Community Manager.
About the badge, no they should not have it. From the description of the badge.
Served as a pro-tempore moderator for a year or through site graduation.
Which means you were appointed by SE and served as a mod on a beta site.
None of those guys asked about fulfill criteria one. (None of them show up in our mods list.) While they have mod abilities, they were not appointed as BSE mods. (Now if SE had appointed one of there own employees as a pro temp mod on BSE, then they would have the badge here.)