Never Trust Your Backups
There was a good write up I read years ago about never trusting your backups. Something along the lines of test, and test often. I do it here at my shop for several different sites. Random files, VHDs, etc. It has saved my bacon more than once and I've seen it do the opposite for those who trusted their backup software when it said it did a thing (looking at you Backup Exec). Just a few weeks ago we had an outage and I was forced to restore 3 VMs from backup. All ended well.
However, for the case of the hospital, how long ago were they infected? How far back do their backups go? Are their backups infected...?