I've booked several times over the years with Amex travel and never had a problem getting MQMs, but the advice above about looking closely at fare designations is probably good.
Also, just recently I cobbled together a crazy international, multi-carrier, split coach outbound, premium econ return for 8 people on ITA.
After trying with all the online engines, DL, AZ, AF phone agents directly and even a waste-of-time try with an Expdia "agent," I thought to call the AX platinum travel line.
The agent was a genius and got me the exact tickets I wanted. I had to pay a fee $29 or $39, I think, but it was WELL worth it.
And everyone got MQMs. (Honestly not sure about MQDs though.)