This is the reply I got from the NMC when I asked:
Good Morning. I reviewed your Merchant Mariner Credential (MMC) and application package after you contacted our Customer Service Center. During that review, I determined that your MMC was issued correctly and in accordance with your request.
Per 46 CFR 501(b) (1):
Each QMED rating must be endorsed separately, unless the applicant qualifies for all QMED ratings, in which case the endorsement will read “QMED-any rating.” The ratings are, Fireman/Watertender; Oiler; Junior engineer; Electrician/Refrigerating engineer; and Pumpman/Machinist.
Per 46 CFR 12.503 (b) (1)
A graduate of a school ship may qualify for a rating endorsement as QMED, without further service, upon satisfactory completion of the program of instruction. For this purpose, school ship is interpreted to mean an institution that offers a complete approved program of instruction, including a period of at-sea training, in the skills appropriate to the rating of QMED.
We no longer issue any unlicensed rating in the Engine department for Engineering Officers 4000 HP or above. If QMED any rating is issued, it is because the mariner has met /tested for all QMED endorsements. Additionally; if a mariner previously held Any Unlicensed Rating in the engine department it will convert to QMED Any Rating.
You fall outside the change in regulations that were implemented on March 20, 20104. To receive QMED Any Rating you would need to complete all QMED exams or a Coast Guard approved program. Please review the most update version of the 46 CFR http://www.ecfr.gov/cgi-bin/text-idx?tpl=/ecfrbrowse/Title46/46tab_02.tpl
If you are interested in being evaluated for any additional endorsements, you will need to submit a new application to your servicing Regional Examination Center with all applicable forms and fees. Thank you for contacting the National Maritime Center.
…and apparently, the fact that all of the qualifying service was earned before March 20, 2014 matters not.