I like the way they do it in the anime much better. Ash made Pikachu learn Iron Tail, Buizel learn Ice Punch and Treecko learn Bullet Seed by training them, tutoring them. I have to say TMs and HMs are just a game mechanic that is difficult to translate into a more realistic medium, like the concept of levels can also be. In the anime, I think they only mentioned levels once (in the very first season at a trainer's school) but the PokéSpe manga has always used them.
If we are to think up some kind of believable way to make HMs and TMs a real thing though, I wouldn't want them to be some kind of DVD disc that the pokémon had to watch. If that was so, there would be piracy for HMs and they wouldn't be so difficult to get and stuff, haha. I kind of like the idea that it's taught through the pokéball somehow, because then only trained pokémon could learn HMs/TMs since wild pokémon don't have pokéballs. And that makes sense imo.
Pokeball turn a pokemon into digital data so go into vitural world that can vist other pokemon if you play pokemon x & y you find out the Pokemon amie 2d spirte is actally inside a pokeball. and pokemon can visit each other if your friend with them
Like that! Since I generally go by the pokéball theory that pokémon turn into energy of some sort inside the pokéball, and X/Y might strengthen this but I don't know since I haven't played those games, I don't think it would be strange if a TM could interact with a pokéball somehow and implement the energy of the move somehow into the pokémon's energy. Isn't this kind of what happens when pokémon are traded (inside their pokéballs) together with items and evolve? :3