I feel like pointing out that Teledgi might not be the only one interested in Omega and the ruins. Ishgard (In face I think it was mentioned in the Coil arc that the Holy See would had loved to get their hands on the Neurolinks, And Omega was apparently created to confront Bahamut), specifically the True Brothers of the Faith, The Garleans who have a fetish for Allagan stuff (and I would not put it past them to have a few people wanting to enslave Erozeans with the same tech used to enslave Dragons) and the Ascians might also know of the ruins

I think it is possible that any of those 3 factions have known about Omega, not likely but possible (But the empire would at least start to be suspicious about the act). That or the Grand Companies are paranoid about 3rd parties such as the empire having an interest in Omega.

Come to think of it, we never did learn how the Triad was felled by the Allagans in the first place, do we?