This same justification was used for obtaining personal financial information from bank accounts (see US v. Miller, 1976).
My problem with this line of logic is that it can be applied to anything not owned directly by the person under surveillance. For example, let's say you rent an apartment. Can the government force the landlord to install mics and cameras without telling you? It's not your property, so do all of your fourth amendment protections disappear?
Indeed. Its okay to search your wallet since its not your "paper", like Constitution says. Its okay to search "your" house, since bank owns it, or landlord. Its okay to track your car with no warrant because well its using public roads. Too "bad" Monsato did not win a claim to patent our DNA; in that case you could be stripped down to naked and shoved with a huge anal probe and feds won't have a problem finding judge who would rule no Fourth Amendment was violated.
Kafka would be proud.