Didn't Ash technically have a Lucario?

[EricaW]

In the movie Lucario and the Mystery of Mew, Ash was given the staff that Sir Aaron put his Lucario in, so technically wouldn't that Lucario have been his for a short time?

[Kenshin5]

People can also make the same case that Ash technically owned Haunter or Larvitar, but did he capture any of them? No... In my mind unless he captures it then it isn't owned by him.