Yeah, well, what can I tell ya. Guess I'm one of the dying breed who believes that there are still absolutes in the universe.
No, it was on a ship. Bashir was beamed out of his bed straight into the holodeck, they didn't knock him out for a day to transport him to a planetside holodeck facility somewhere.
Section 31 might have access to a Dominion transporter capable of beaming someone over the distance of several lightyears.
And "Journey to Babel" too - as Sarek had no issues lying to, and keeping secrets from his own wife because in his mind, logically, she could do nothing to help with respect to his medical condition, and therefore didn't need to know. Marcus wasn't building towards an insurrection per se, he'd just designed and built a ship 100% designed for war, and put things in motion to have the Federation START a war with the Klingon because he thought said war was inevitable; and in his mind it's better that Feds start it (in hopes of controlling the pace/direction instead of waiting for the Klingons to start it once they're ready
For all we know, Sloan's holodeck was a simulation being run on one of Quark's holosuites! We never saw his "Section" in action: his colleagues were holographic, his missions conducted by patsies, his knowledge of secret things never explicated. He did know how to cure Odo, but not because he was Section 31 - but because he knew how to get to the secrets of Starfleet Medical, which is a different thing altogether. The Sections in the previous centuries seem to be the real deal, even if somewhat different in the 22nd and 23rd. The Section might be dead by the 24th, though, save for lone reenactors. Timo Saloniemi
I doubt the cover story was that Stargate=Space Radar Program. Instead, the cover story was that Carter was working on space radars. And the cover story of O'Neill, or at least for those who actually died offworld, may have been that he or she was in Absurdistan doing top secret hostage rescue (but we never told you so). A tailored cover story for everybody, none of these linking them with Cheyenne Mountain or even each other in any manner. And a flexible one at that, so that a colleague accidentally spotted by an outsider would become a "colleague" on the spot, despite having a different cover story for other folks. The Space Radars were just the common cover in the Carter context. Timo Saloniemi