I don’t think that’s the same. I had a hotel booking at a SHA + and I emailed them yesterday to ask if they were an alternative quarantine hotel as well and they said no
because it’s a liability for practices and there is very little upside. He has the positive test result which is all that they require. Typically the way that it would work is you go to a doctor, show them the positive test from a couple-few weeks earlier and then the check that you’re not symptomatic and issue the letter. If I was American, living in Houston and dealing with our family doctor, it may be a bit different.