Was a little confused by that. Arya was taught by Serio and probably get some pointers from the Hound. The Faceless Men never taught her to swordfight. The Waif pretended to train her in quatersfaffs but that always ended in the Waif beating Arya up.

I think she was referring to the dodging maybe.

It's true that no one person taught her. She has definitely picked up things from at least several different people. However, if I remember correctly, the Waif reported to be "no one" just as their leader did and just as they wanted Arya to. Wasn't everyone in that organization/club/assassin guild supposed to be referred to as "no one"? Also, I'm sure there was more to Arya's training than what was shown on-screen. Even while getting beat up, you can learn lessons in combat.

I did notice one resemblance. When Brenner knocked Arya onto her back, Arya leapt to her feet and went on the offense again. She did the same trick once with the Waif.