Watch the video at SW.C "getting a wedgie" it shows the droid you speak of in Obi's ship.
Also re-watch ANH. Obi never says he dosen't know R2, in fact he says "hello my little friend". He tells luke he "never owned a droid".
TRUE.
Padme owned R2, and ANi owned 3PO.
Remember you have to see the OT from a 'certian point of view'.
I'd never seen the Jedi as being that posessive. I thought they just had their living quarters, their clothes and their sabres. Anything else was taken for special missions from storage. It would seem like there was too much of a superiority thing going on if some Jedi got their own ship, droid, etc.