Talking to some drivers yesterday who thought you didn't have to hand the papers the doctor fills out regarding your physical, saying the doctor submits them now.

Not exactly. As of this past February, the medical examiner must send the Medical Certificate electronically to the National Registry which then forwards it to the given state's DMV.

You still have to turn in all completed paperwork to Pioneer. It's just that it's no longer their job to send the medical certificate to DMV nor can you any longer do it online. 

https://nysbca.com/News/13599473

Got an email from the DMV (time stamped 2:04 this morning) that my medical certificate has been up dated. I guess the system works.

To get such notifications you have to register with MYDMV ... https://dmv.ny.gov/mydmv/create-an-ny.gov-id . Choose to get electronic notifications and you'll get reminders when your personal vehicles are due for inspections or registration renewals.