It is possible that in AC2003, you need to have exclusive access to make this work even though you are a member of Admins group. Lots of changes have occurred since AC97 and AC2K, where ownership of the overall DB was (slightly) less significant a security issue.
To get exclusive access, your admin account has to have the right to OpenExclusive in the permissions list for the database object. Then I believe you have to open the DB by opening Access first to get the DB selection dialog box; then you have to check "exclusive" or whatever it offers to that same effect. Then open the existing DB. OpenExcl will be denied you if anyone else is still in the DB at the time.
As to the rist of having a DB with the DB Object's owner "Unknown", that is a limited risk as long as you let the system generate new SIDs each time you create a user. (As opposed to manually choosing one each time.) That gives you a good chance that the SID (an internal binary number that identifies each individual username) remains unique. And if the owner SID is unique, having an unowned DB is not a problem short-term... as long as you still have access as an admin-class user.
Long-term, it is time to copy out the DB to another .MDB file and update the db object owner that way. But if you need to delay to a "convenient time" that is OK.