D.A. fan is back for an ME1 Text Only 'Let's Play' (page 51)

Admiral Hackett asks Shepard to rescue one Dr. Amanda Kenson from the Batarians, who have arrested her under charges of terrorism. After rescuing Kenson, she takes Shepard to her research base, where she and her team have studied a reaper artifact they refer to as Object Rho. Kenson tells Shepard that the reapers are mere days away from pouring through this system's relay, called alpha relay, and would spread over the whole galaxy from here. As a last desperate way of delaying them, the asteroid the research base was built in has been fitted with thrusters so it can be launched into alpha relay to destroy it. However, since then Object Rho has indoctrinated Kenson and her entire team, who now await the reapers' glorious arrival instead of wanting to stop them. Shepard is overwhelmed, sedated and imprisoned but manages to flee soon after regaining consciousness. With mere hours left until the reapers arrive, Shepard activates the asteroid's thrusters. Since Kenson had cut all communications after Shepard's escape, there is no way to warn the 300,000 Batarian colonists in the system, who all die when alpha relay gets hit by the asteroid and explodes moments after the Normandy escapes through it. Shepard reports to Hackett and is informed that there will be an investigation on Earth.

Yes, the dialogue with Anderson is different depending on whether or not the player did the DLC. Anderson just says "The shit you've done, any other Alliance officer would be court martialed and left to rot in the brig." If the player did not do the DLC, it is absolutely confirmed during the Ghorek side-quest later in the game that the Alliance destroyed the Relay, not Shepard. In that case, Shepard is aware of the event, but clearly had no participation in it.

Isn't it also mentioned in a codex entry and/or the war terminal? I seem to remember it "reducing" one of the Alliance assets.

With Arrival, it makes sense as Hackett outright tells Shepard they probably will have to put all the blame for the mess that happened in the Bahak system on Shepard alone in order to avoid all out war with the Batarians. Hackett basically asks Shepard to come back eventually and take one for the team on this one. A paragon Shepard would probably do that. The only weird thing about it is, if you play a renegade Shepard, you might not think it would fit Shep's character to just submit to the Alliance and let yourself be arrested. In this case, somehow, the Alliance must have captured you, which means they must have been able to find the Normandy despite its stealth capability. Given that the Alliance and the turians developed the technology in the first place, thye may have found a way around it but in any case, how exactly Shepard got arrested is never made entirely clear AFAIK.