maybe so , but it seems like all the jedi fighters had an R$ unist of srts, so by the show and simple reasoning you'd think Anakin would be assigned such a driod, and we know R2 was assigned to Padme along with C-3PO, so it thats why i think both Anakin and Obi-Wan never owned R2-D2, in my own opinion
actually...R4 is not completely an R4...It's an R4 modified. Cause R4's have different domes, different shapes. It's an R4 with the dome of an R2. So my guess is if you really want to follow expanded universe...most jedi starfighters had R2 units not R4's...you just have to know what you think is canon and what is not.
and we know R2 was assigned to Padme along with C-3PO
When is 3po "assigned" to padme? Anakin builds 3po, then he retrieves it when he goes to tatooine.. and then 3po stays with both of them... c3po isn't really "assigned" to padme... I think that anakin leave the droids with her because he, as a jedi, cannot have any property.
I honestly think he was"joking" with R2. Both of them knew each other and what the deal was. R2's response may have been something like "Damnit old man, I had to tell them you were my property so I could get here. Better story than YOU would have come up with." or another crabby/clever R2 retort. Similar to the Yoda/R2 thing with the flashlight on Degobah. If it was just some creepy green swamp dweller, when Yoda started hitting R2, out would have come his tazer (A La S. Crumb in ROTJ.)
Granted, R2 is a droid and I'm applying a lot of personality and reasoning to a character we couldn't understand when he spoke, but his actions and beep tones really gave R2 a deep personality.
Carnage
well....i mean, how are you supposed to recognize a astro droid anyways, R2 was a blue atro droid, im pretty sure theres more then 1 blue astro droid. i mean, they all look exactly the same. he wouldent remember it untill he saw the message from leia. then he might have an idea. cause i dont think luke says R2-D2 to obi wan. i believe he says "little droid". so there is really no way that obi wan would just "think" its the same R2 droid.