Can a doctor diagnose EDS based on diagnostic criteria alone?

I don't qualify for genetic testing through my insurance. I am wondering if a rheumatologist is capable of diagnosing me based on diagnostic criteria, without the gene testing. Does anyone know if that's a thing. At my appointment a few weeks ago the doctor told me to get tested for Ehlers Danlos through a genetic doctor, but my insurance only covers cancer screening. Meanwhile I have no answers.

https://preview.redd.it/sztzjhcba9ng1.png?width=1760&format=png&auto=webp&s=16db792b9933a9b33018f6b412c805326ae0fadb