Can a MM download, being sent to one phone, also go to a third party who is concurrently sending the mutual receiver a text message?
Yes, this was possible on Android 2.2 owing to an error in Android. On versions with the bug, if you receive an SMS (or MMS) message while composing another, the message being composed has its recipient replaced with the sender of the message you received.

It was fixed in Gingerbread, as well as with an update to Froyo, but not all manufacturers or carriers may have passed the fix onto end users.