Someone offered a very sensible explanation a while ago.
Remember how Okido had three other, empty balls in his lab as well, ones the three other starters had been in before they got taken? These three balls, which had the Pokemon's names written on them, remained behind in the lab while the Pokémon went with its Trainer, and were presumably going to be used for storing new starters later. Apat from the fact that Pikachu's ball had a thunderbolt on it instead of the name "Pikachu", that should be the case with that as well.
So the thunderbolt-marked ball is still at the lab together with those other three balls, while Satoshi and his three rivals were given new, unmarked balls for their Pokemon as they left the lab.
Makes sense, right?
Remember how Okido had three other, empty balls in his lab as well, ones the three other starters had been in before they got taken? These three balls, which had the Pokemon's names written on them, remained behind in the lab while the Pokémon went with its Trainer, and were presumably going to be used for storing new starters later. Apat from the fact that Pikachu's ball had a thunderbolt on it instead of the name "Pikachu", that should be the case with that as well.
So the thunderbolt-marked ball is still at the lab together with those other three balls, while Satoshi and his three rivals were given new, unmarked balls for their Pokemon as they left the lab.
Makes sense, right?