The more I think about this, the less it makes sense. If Erik wanted Logan for some reason, he could just fish Logan out of the river himself. (Does Erik even know that Logan has healing powers? Because if not, there's no reason anyone would realise he was even still alive.) And no one else should have any idea Logan's down there.

Even if Erik offhandedly mentions, "Logan? Oh, I threw him in the river", why does Mystique want him? Unless she's working with Charles... Which would make more sense, actually, because Charles knows Logan has to be alive and would want him back, yet can't very well just go dredge the river for him. Mystique can do it under some kind of official guise. But if it's just a case of getting Logan out of the river, why pretend to be Stryker specifically? I guess Mystique may be keeping an eye on Stryker's activities, but... The pieces don't seem to fit together.

What you suggested about the eye flash actually makes much more sense. But I'd tend to assume Singer has plans to pick up on all this in the sequel. Maybe.