When you're in the hospital after you've been mugged, have lost your wallet and 75-item keychain and are asked for your insurance info you can answer "Sure, can I use your computer or smartphone?"
Try that if you're one of the folks checking into a hospital right now up there in the northeast, in the electricity void following storm Sandy.
Luckily, hospitals are required to treat your true emergency conditions with or without insurance. That all gets sorted out later.
I can't imagine any hospital allowing you to insert a thumbdrive into one of their computers. If they do, and it actually works, their I.T. department is a bunch of idiots. They may even block you from accessing cloud storage, but I don't know about that. At least using one of their in-hospital computers all this should be blocked, and they should not even allow you to touch one of their in-house computers. They may have DMZ computers, off their LAN, that they will allow you to use. But with the advent of smartphones and the ability to access the internet via 3G/4G, the need for a dedicated computer is diminishing for some things. For things like insurance numbers, why not encrypt them right there on your smartphone? Adding cloud storage into the picture just makes you dependant on another layer of technology maintained by a third party out of your control.