Now that Legends is showing how early pokeballs worked, it seems like they eventually got safety features built-in to them for modern times. In Legends Arceus, pokeballs are just wood and metal that store a tiny version of a pokemon and certainly can't be pushed into any "PC" or be taught moves through "Technical Machine" discs. In modern times though the pokeballs convert the pokemon to data to allow them to be easily accessed across the world after uploading them.

I'm thinking that modern pokeballs register the true owner of a pokemon and the software on them will refuse to capture any pokemon that is already registered to another user. The snag machine in Colosseum and Gale of Darkness converts pokeballs to "Snag Balls" which might just be that it overwrites that safety program and can overwrite any pokemon's true owner (though Michael has a Snag Machine that still has restrictions where it will only work for Shadow Pokemon. Wes has the only true DRM-free snag machine)

In Legends Arceus your character will flat out refuse to throw a pokeball at a pokemon a trainer owns. If they did, though, it'd probably work.

It'd be interesting if this was true though, that the global Pokemon League Corporation has these various rules in play, controlling the main way people are able to live their lives. Don't forget too, it's their rules that make it so a seventh pokemon in a trainer's possession gets immediately and forcibly uploaded.