Sharing something in Sanguis Astroism (for instance) would make it public knowledge in multiple realms, so I think we're covered. I don't see a reason to be more precise in the wording. If anything, I should probably remove the reference to realms and leave it at "public knowledge." Then the Moderators can make a call if someone complains.
Thus speaks someone with an Astroist bias, methinks
If something were shared in SA, people in multiple realms would know it, but it would not necessarily be public knowledge within those realms. For instance, many people in Luria would know it, but Alanna—their ruler—would not.