Spoilers! That’s kind of her thing, right? Not revealing anything ahead of time. As far as Amy and Rory knew, River had no reason to be particularly close to them. If River were to act particularly close, that would raise suspicions - and she already knows when they find out the truth: at Demon’s Run. If they were to learn the truth earlier, that would be a paradox.
I’m really glad they kept that opening scene with Rory and River, because that really solidified my opinion on the matter. Did you see that look on her face, when Rory introduced himself? Did you hear that tremble in her voice, when she said “hello, Rory”? If we presume that she’s moving pretty consistently in reverse-chronological order to the Doctor and his companions, then Rory introducing himself as Rory - instead of, say, as [X] - tells her that from now on, she’s going to have to pretend that Amy and Rory aren't [X].
Look at earlier stuff - how perfectly, momentarily confused she is about “the centurion”, how neutral she is to Amy until that angel’s in her eye, at which point she's all hugs and soothing words. Looking at it through the context of “A Good Man Goes to War”, I don’t see her as bizarrely indifferent; I see her as unwillingly keeping her distance, knowing that this is how it has to be.