GP is not appealing to authority, he/she is advising caution based on the fact that HN is not largely made up of medical professionals.
That is an appeal to authority.
You're wrong
"Someone who has gone through years of medical school to get a degree is more likely to be correct on matters concerning medicine than someone who has not" is not an appeal to authority.
Advising against blind trust in non-experts' statements doesn't imply a recommendation to blindly trust experts' statements.