I know that the way to get a Careers 2.0 invitation is secret. However, I'm wondering whether it is public knowledge (or can be revealed) whether activity on sites like Unix & Linux and SuperUser and Programmers can count toward an invitation to Careers 2.0? It would seem rather narrow to only factor in StackOverflow.
Only activity on Stack Overflow counts toward invitations to Careers.
Stack Overflow is the only site which is entirely for technical problems related to programming. Other sites on the network might dip into that category, but are not specifically built for it.
If you are truly interested in getting an invitation to Careers, activity on Stack Overflow is not the only avenue, though it is likely to be the fastest for anyone who is a programmer.
Essentially, it seems the way to get an invite, as briefly hinted in the secret you received, is to get a lot of reputation on a single tag on Stack Overflow. Other sites don't count, however, you can link questions from other sites in your Career's page.
Bottom line is, if you want to get a job as a programmer from Stack Overflow, you really need to show you know something from a particular tag on Stack Overflow. But once you are in, you can use questions from other sites as well.