I personally doubt that Google monitors/records voice conversations. IANAL, but some states have "all party consent" rules (sometimes called eavesdropping or wiretapping laws) where all parties to a conversation must agree to information being recorded. Even if the GV user agrees to terms that allow monitoring, the person on the other end might not agree to those terms.

Many doctors don't give out confidential information over the phone at all.

It is kind of funny seeing all this concern over IT privacy while other forms of privacy aren't taken nearly as seriously but are probably more important (as one of the previous posters mentioned-documents face up in passenger seats of parked cars, "attorney eyes only" documents being read by attorneys on airplanes, etc...)

Also, just FYI it's HIPAA, not HIPPA

I 2nd jetsfan92588's sentiments... IANAL, and while I am generally more paranoid than average when it comes to this stuff, I do think google would be making a big mistake if they were, in fact, recording conversations (as opposed to recording voicemail messages which are transcribed). Reason being those all-party consent laws in many states. Again, not talking about federal wiretapping, just private industry here.

Analog lines are really easy to tap with analog equipment, and I could be sitting outside your house or in your building's phone closet, or who knows where else.
VoIP type lines I'm sure have their own weaknesses as far as packet sniffing and reassembling, or even software intentionally recording calls. Both are insecure, have laws surrounding the issues, and could probably apply HIPAA standards for phone use to either if analog vs digital/voip isn't specified in the document.

The fact that the medical professional is concerned at all about GV privacy should be enough to clear them of any wrong doing "if" someone were to data-mine their conversations. The probability of this occurring with GV is slim to none, though that's a different story with voicemails. GV has a direct connection that isn't recorded when two people are talking, but is recorded and transcribed when a voicemail is left. So as long as the clients aren't leaving voicemails containing PT info on the dr's GV then they should be good.