I'm surprised no one has yet created a database where people can anonymously submit ranges of IPs where a lot of users are on IE7 and other older browsers. This would paint a big ol' bullseye on those organizations since it highlights them as easy targets for exploits that target older browsers.
The newer browsers actually come with a lot of feature-induced security problems too. Microsoft continues to release security updates for IE7 so it might be better to use than a newer version of IE that could have HTML5 exploits.
You can take it from the other end. These employees are locked on IE7/8 because there's not enough external forces to make it a business issue. When they won't be able to use critical resources because of their browser or OS, the upgrade will just happen, how painful and costly it will be (as long as it's less costly than not accessing the said resources)
Actually I agree with this line of thinking. I we could in fact fork IE7, replace it at the system level and people were enthusiastic enough to patch bugs and security holes forever, why not.
From what I understand, there's a reasonably large market for temporary nurses, for times when a hospital is understaffed. I suspect it's acceptable to look for a new gig before your current one ends.
Edit: It also looks like hospitals, not nurses, are the actual customers.