Security should not be a concern with using Google Docs platform. You can restrict the access of any template or your google drive folder where templates are being stored, see this article for more detail. You can make sure you are HIPAA compliant.
In addition, here are some other helpful articles on Google security:
Google Cloud Platform Security compliance: https://cloud.google.com/security/compliance.
Link to FAQ document regarding Google Security: https://gsuite.google.com/faq/security/. You can find related question and go to drop down for more information.
Statement from Google on G Suite security and trust:
Google started in the cloud and runs on the cloud, so it's no surprise that we fully understand the security implications of powering your business in the cloud. Because Google and our enterprise services run on the same infrastructure, your organization will benefit from the protections we've built and use everyday. Our robust global infrastructure, along with dedicated security professionals and our drive to innovate, enables Google to stay ahead of the curve and offer a highly secure, reliable, and compliant environment.