This part seems interesting:
"A couple of years back TrekMovie spoke to Bryan Fuller about his idea for a show, which he envisioned would be set in the new movie universe, but not on board the USS Enterprise."
Since that would have been the very first (and only) time were it was confirmed that Fullers' idea would be set in the JJverse. But if you click on the link, it leads back to an older article with the much more familiar piece where he said the JJverse is "interesting", considering "how TNG would have evolved in this universe".
My guess is: Fuller has (and had since then) an idea for a show in a post-TNG setting (there is an older interview with him already porposing an actress as the new Captain). That idea would of course be adaptable for the equivalent of the TNG-era in the JJverse. That's why he was tip-toeig around to question, to leave both possibilies open for whatever the powers-that-be will decide. That means, he's pitching the basic concept of his new show. The producers at CBS can then decide wether it takes place in the new continuity (recent success), or the old one (50 years of success). In the case the producers are undicisive (evenly likely), the ball goes back to Singer. He has to check his chioce with Kurtzman, but since Kurtzman was never a die-hard fan anyway, I guess he's more interested in the actual producing part, leaving his mark on the actual show in whatever fictional continuity it will take place (and from interviews back then, it seems the one with the original idea for the timeline split was probably Orci.)
That would leave SInger (the one who actually envisions the new show) with the decision where to set the new series. In the new continuity (either in the "present" or the far future of it, leading to an MCU-style large universe, where the show needs to subordinate to the creative decisions of the movie people), or to the old universe, on which he already worked on, and in which he probably envisioned his idea for "his" show before the reboot even happened.
Or, and that's what I think is most likely, set a bit after the TNG era, in an "arms-lenght-reboot", that could pass as a continuiation of both universes on first sight.