As an employer am I required to verify that the driver obtained his physical from a doctor on the DOT National Registry and note it in their driver's file?
Yes, this can be done with a company form you developed or even noted on the physical form under the doctor's registry number, date and signature you verified.
Here is a more detailed explanation from the Electronic Code of Federal Regulators:
391.23 (m)(1) The motor carrier must obtain an original or copy of the medical examiner's certificate issued in accordance with §391.43, and any medical variance on which the certification is based, and, beginning on or after May 21, 2014, verify the driver was certified by a medical examiner listed on the National Registry of Certified Medical Examiners as of the date of issuance of the medical examiner's certificate, and place the records in the driver qualification file, before allowing the driver to operate a CMV. To view more guidance on section 391.23, click here. For more information on common help desk questions, visit our Compliance and Regulatory resources page, by clicking here.