Using the author's preferred restatement in the comment:
Is it okay for our IT support contractor to have the ability to remote in without authorization?
Under normal circumstances, Yes.
Let's talk about the specific key words.
Assuming you don't work from home, remember that the IT Admins can sit in your chair at the end of the day and login to your workstations, install updates, and re-image your computer after you leave the company. They already have full access to your computer and can (typically) view everything on it. It's possible they have access to the company databases and health records too, and so there likely is nothing they could possibly see on your screen during a remote session that they wouldn't already have access to outside of the remote session, if they decided to view it. If that's the case then asking for your permission before taking over your computer could be thought of as more of a courtesy, rather than a legal requirement.
Many contractors work as an extension of the company, and have to sign NDA's, HIPAA disclosures, attend training, and follow the same rules and laws regarding security, privacy, and ethics that all of the employees do. Even in a situation where a contractor was not asked to sign anything, that would not grant them permission to break the law.
Note: these statements are generalizations which may apply to the healthcare industry, but don't necessarily apply to all industries. For example in the defense industry you might not allow an IT person to remote into a machine without user interaction in case the user is viewing a document that is above the clearance level of the IT person. (Though this isn't a problem if there are dedicated rooms with machines specifically for viewing top secret documents.)