The process is the same in all visa offices. With an operation manual which all visa offices have to stick to, this is our situation, New-Delhi and Beijing process applications in 5 months and Islamabad in 26 months, so imagine if every visa office worked with different regulations based on what their mood was, omg what would happen then!!!!
Anyways, yes, the doctor forwards the results to the regional office responsible for medicals, Paris/London/New Delhi etc. (which in our case is Paris).
Paris sends the results after 2-3-4 weeks processing to the visa office (Ankara/Amman/Beirut). There is this green slip the doctor gives to the applicant after the medical exam, which we scan and email to the visa office just as a proof that we have done it, the real and final result is forwarded by Paris to the visa office. So even if someone doesn't send in the scan nothing will really happen since the results are automatically forwarded from Paris to the visa office, but there's no harm sending them a proof that you redid the medical.
Although keep in mind that if you were advised by the visa office to redo your medical, there might have already been a form attached in the email they sent you and in that case the doctor will not give you anything to scan and send! So this green sheet I'm talking about is for the people who go ahead and redo the medicals without waiting for the embassy's email, like me