Yeah I noticed that too when I saw whatever episodes those were. I personally don't think that this was some innuendo to someone else teaching her to fly the Tardis but just a little mistake the makers of the show made. I mean, earlier in the show the doctor says that hes the only one who can fly the Tardis and we've seen that that is not true. And lastly, it wouldn't be the first time that River has lied, so who really knows. Even though we have learned a lot more about her recently, we still don't know a lot about her.
At first I took it to mean that Amy had been taught to learn to fly the TARDIS in an emergency situation and then taught River, but then after The Doctor's Wife rolled around, I sort of just assumed that River found a way to communicate with the old girl better than the Doctor. I don't think it was a mistake for her to say that the TARDIS taught her in the slightest; in a way, River serves a lot of similar purposes the Master serves. She's meant to balance the Doctor's brilliance, which is why she makes such a compelling counterpoint and romantic interest to him. She makes herself an equal and is able to keep up with him, so it wouldn't be much of a surprise if she found a way to learn from the TARDIS.
Actually, she didn't say the Doctor taught her. She said she "learned from the best" and followed it up with "Sadly you were not there that day," implying that it was NOT the Doctor who taught her, that he is not the best, and thereby, making an edgy flirtatious jab at him like she usually does. If I remember correctly.
'Kay, re-reading the post... I don't remember her saying the Doctor taught her outright. I'd have to find that episode you're referring to.
I think the "shame you weren;t there that day" was a joke, intended to deflate his confidence/arrogance. Alternatively, it could just be a different incarnation of him.
"I'm flying it perfectly! You taught me." --River Song, The Pandorica Opens
"Oh, I had lessons from the very best. It's a shame you were busy that day." --River Song, The Time of Angels
Of course, the Doctor was busy *dying* "that day," that day being Let's Kill Hitler. I assume the TARDIS taught her the basics and later the Doctor (when he was not dying) taught her the more complicated maneuvers.
Yeah I think that makes sense especially since we never know how far into the Doctor's future the River we are seeing is from. So it isn't difficult to believe that the first time she said something, she had not been taught how to completely fly the Tardis yet.