After a bit of poking around, it appears that the WD Smartware encryption is just standard AES encryption. The Smartware seems to be a backup and maintenance tool that uses AES encryption. Here's some text from WD:
After configuring the software the very first time you boot up the drive, SmartWare will run automatically (if you allow it), providing an automatic and continuous “backup and drive management” solution. The software comes built-in, i.e. it resides on a separate partition on the hard drive, but the auto-backup can be disabled.
As for the “safer” attributes of the new drives, each one comes equipped with WD Drive Lock – password protection + 256-bit hardware encryption. Once the password is set, the owner (or anyone who knows the pw) is the only person who can access the data. If the password is lost, there is NO way to retrieve it because the password is never shared with Western Digital in any capacity.
Beyond the password, every bit of data stored on the drive is protected by 256-bit AES encryption. In other words, without the password, the data is basically impossible to access. Might sound a bit over the top, but WD said they wanted to err on the side of total security.
Lots of marketing reselling AES drive security if you ask me. That's from this page. So I don't think their encryption is any better than regular AES. Also, here's the link to wikipedia for AES Enctryption.
Additionally, I'm with oranges: the hospital probably has rules and regulations to govern this. I think you're being a great help. The fact they think it's "more than adequate" tells me they might be seeing it as better, which it isn't. It also might mean they see that it has standard AES and that is more than adequate.
Good luck. Tread carefully!