Once the government has it, it’s not secret to those in government. And there millions of them.
Are such precautions paranoid? Hardly. WikiLeaker Bradley Manning showed how incompetent the government is at keeping its own secrets; incidents where various agencies accidentally disclose personal data like Social Security numbers are legion. And that’s not to mention the ways in which commercial databases are prone to hacking and/or exploitation.
Be careful about sharing your medical secrets with Uncle Sam.