A few things came together to make this possible.
Area 51 periodically pulls a list of sites through the API and updates its own internal records. So it happily created a record in its Sites table for docs-beta, even though there was no actual site proposal to go along with it.
I didn't realize that happened, so didn't flip the State that record to indicate that the site was no longer in private beta. (That part apparently doesn't get updated via the API. It just checks for new sites, IIRC, not doing a diff on what's going on state-wise.)
But on top of that, Area 51 also maintains a list of site associations for each user in JSON format, including site's id, the user's id on that site, and the user's reputation. This is where this gets fun: because of the site record created above, A51 dutifully made requests to the docs-beta site asking for users' reputation... and we just as dutifully redirected those requests to Stack Overflow. So basically everyone with an SO profile ended up with an effectively duplicate association record, regardless of whether they even joined the docs-beta site or not.
Site record has been updated in Area 51 and associations regenerated, so everything should be back to normal now.