The Puppetmaster
I'm Alive
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Ash's bulbasaur is an excellent example of this, since we got to see it learn dig while at Oaks. Granted the situation was a bit special but that doesn't mean it's impossible for the pokemon to learn new moves when they're not with Ash.
Then we have Buizel. Buizel loves to train and has learned every move he has except for ice punch before he ever got a trainer. If he gets any air time during Best Wishes it wouldn't be much of a surprise if he's got a new move or two. The same goes for the rest of Ash's pokemon, there's no reason they can't do a little training on their own time.
Actually Buizel learned Water Pulse during Ash's gym battle against Maylene (but Ash didn't train it to learn it). Also, it forgot that move for Ice Punch so I'm not sure if that's why you discounted it.