Aha. The problem here is, I think, not that you hadn't bought music on the other machines; it's that the other machines weren't connected to Ubuntu One, and buying music connects you to Ubuntu One. If you have a fourth machine to test with (!), then if you connect that machine (Me Menu > Ubuntu One > Devices > Connect, or "u1sdtool -c" from a terminal) then that machine should also get the music without having to buy a new one.
Aha. The problem here is, I think, not that you hadn't bought music on the other machines; it's that the other machines weren't connected to Ubuntu One, and buying music connects you to Ubuntu One. If you have a fourth machine to test with (!), then if you connect that machine (Me Menu > Ubuntu One > Devices > Connect, or "u1sdtool -c" from a terminal) then that machine should also get the music without having to buy a new one.