"The greater good" is a recurrent theme throughout Stargate Universe's two-season run. In the episode "Air Part 2" the core series theme comes into play really for the first time.
"Air Part 2" finds the survivors of Icarus Base beginning to explore the ship they must now call home. Realizing that their air supply is beginning to go due to a weakness in the shield protecting the ship's damaged hull, they must plug that leak before the air runs out. And they don't have much time.
They discover a significant leak in the hull of one of the ship's two shuttles. But there is an additional problem. Closing the door would solve the problem, but the breach cannot be isolated and closed off except from within the shuttle itself. The door can only be secured by someone willing to remain inside the craft, essentially committing suicide. Once locked inside, no egress back into the ship is possible. If it's not done, all of them will all perish very quickly as the breathable atmosphere escapes into space.
The Icarus survivors are barely a crew at this point. Leaderless and still stunned, there is an immediate vaccum at the top. With Col. Young (Louis Ferreira) still badly injured, and his appointed leader Lt. Scott (Brian J. Smith) not very experienced and thrown suddenly into an impossible situation, Dr. Rush (Robert Carlyle), claims control, stating that he has been appointed leader of the de facto crew by Stargate Command back on Earth.
Having used the communication stones, a neat bit of Ancient technology that allows the consciousness of two people to be swapped, Rush has indeed been back on Earth, meeting with Gen. O'Neill (Richard Dean Anderson). Although this meeting is not shown in the broadcast episode; we do see at least part of it in the extended version of "Air," available on the Blu-ray release of season one. But even in that version, we do not see O'Neill do anything of the kind. And when Rush attempts to assert his supposed authority, no one accepts it (and who would, given his role in creating their predicament in the first place, not to mention the way in which he addresses them as a group?) The other civilian leader aboard, Camille Ray (Ming-Na) refuses to recognize Rush's authority, but doesn't claim it for herself either.