We have been shown ZERO to suggest she is "probably better trained than anyone", so I can't even imagine why people keep saying things like that. All of the knights, Dothraki, mercenaries, etc have done nothing but fight and train to fight their entire lives.
Arya took a few lessons at 8 years old, then had no training whatsoever for years while she was a captive in Harrenhal, captive of the Brotherhood, captive of the Hound, then had some staff "training" at the House of Black and White for however long she was there -- but she was not being "trained" to fight, merely beaten up until she could slightly protect herself as a form of self-preservation. She was expressly forbidden from touching her sword, we never saw Jaqen or the Waif use any sword, we saw no swords in the House of Black and White. The only time the Waif even used a knife was to gut Arya and the actress, otherwise we saw no knives in the House either. Yet somehow Arya is a master swordsman and knife thrower after leaving.
Meanwhile we see Jon training repeatedly, we see Brienne training, we see Jaime training, we see the Mountain training, and we know these guys have been training -- and fighting for real -- for their entire lives. We have probably literally seen Podrick training more than we have seen Arya training.
....this aside from the obvious logic that it's moronic to think Faceless Men would be great hand to hand combatants. Their whole point is to be invisible assassins, not warriors. And if they are training to make magic face masks, assume new identities, make and use poisons, change their voices, serve their God, deliver the "gift", clean the temple, etc etc, how could they ALSO train enough to be the best swordsmen when so many others train ONLY for that? It's absurd in every respect.