The following is the law and will be a dry read.
http://www.hhs.gov/ocr/privacy/hipaa/understanding/coveredentities/hitechrfi.pdf
As I understand the law doesn't require you to implement any specific system but rather requires the system to anticipate and protect the privacy of medical information. It is on the you to interpret what it means to protect the privacy of medical information.
In your example your client is connecting to a server over a VPN, which I assume that traffic is encrypted, to pull medical information. Your question is whether the computer needs to have its drives be encrypted?
That to me would hinge on whether the data is stored (file saves, copy and paste, temporary files) on the drive of the computer. If so then encryption would be my recommendation.
Additionally access control is a consideration. It would circumvent encryption and passwords if the operating system and/or software were configured to auto decrypt the drive and store the passwords allowing unauthorized access by individuals who don't represent the company to the data. This would extend to the user keeping stickies with their passwords attached to their monitor or under their keyboard.
In summary you're asking what HIPPA's requirements are. Those requirements, as I interpret them, is for a company or organization to develop procedures to reasonably prevent unauthorized leaks of private medical information. What I think you're looking for is best practices for solving this problem. Lance's links are very good at answering that question. The ultimate goal is to prevent medical information to be leaked.