>>22636
It's true that in the anime, there is barely anything to hint their relationship. However, I do remember some very subtle hints in this episode. Like when they came out of the apt., Koizumi was looking at Nagato as if for approval, but she walked away. This shows that Koizumi is at least interested in Nagato, but she either isn't allowed to build a "link" with him, either just doesn't want to. I don't remember where exactly, but there was a scene where Koizumi is seen discussing some computer stuff with Nagato. He was very close to her. This is somewhat unusual because he often prefer keeping a distance with others except someone whom he is really interested in, like Kyon. Remember how in at least 80% of the pictures, he's in the background, at least 1.5m from the rest (Kyon excluded)? Yeah, he's that kind of person. So if he's physically close to someone, he's emotionally or intellitually interested.
In the novel, Snow Mountain Syndrome chapter, Koizumi swore that if anything might menace Nagato's existence, no matter how good the situation would be for the Agency, he will betray his organization and help Kyon to help Nagato.
So this couple is not totally off-canon, but you're right that one picture with them simply standing beside each other doesn't prove anything.
(I'm still with Itsuki/Haruhi/Kyon.)