Actually, no. And that is the beauty of it.
The actual balance is stored by the whole network, not on your physical computer. So by "sending" bitcoins, you don't really change their physical localization. It's just matter of complex mathematical computations.
By sending Bitcoins, you give somebody else the rights of ownership to the bitcoins, but they don't move themselves.
This all depends on the final legal status. Law is known to not care much about technical sense.
It's not really "technical", its real.
Bitcoins are physically not stored on anybody's computer.
The private key giving you access to certain amounts of BTC should be viewed as a digital "certificate of ownership" of bitcoins, not bitcoins themselves - it's completely logical.