If the car was driven on to a flat bed, that pretty much rules out a blown universal joint....in that case the majority of torque will transfer to the Pushing wheels (rear) there would also be audible sound as in crunching, clanking....you did not mention any sounds of this nature....I doubt it's a shift fork (in automatic transmissions, they are always preloaded and lined with the next cog (gear)...The bigger question is why it died in the first place....then was able to restart, that rules out timing...spark ignition is directly tied to cam gear,cam gear is coupled to slotted key in cam...yet it started fine, weird!
You'd have to run some tests to determine...starting with ignition and firing, look at electrical flow to ignition modules....it could be something as simple as loosing contact, a connector is not quite making proper contact, under load such connections will arc rather than transfer and would shut an engine down.
None of this makes sense without testing protocols, your car is way too new for this to be component failure,although I saw stranger things happen with new cars...
Did you notice any thrown codes displayed in the dash area, next to the check engine light? something beginning with P followed with a E then a number (number indicates frame line in CPU module).... please keep this thread updated Rock...it sounds like this should be quite easy to trace, especially is codes were triggered ( I'm willing to bet there will be multiple codes read)...
Hope it gets resolved immediately for you...fingers crossed, and as expressomac said congrats on your MKC!