No heat from driver's side?

Your description sounds like the left hand blend door is either broken, the linkage is damaged or the actuator is faulty. To test which it is you can remove the panel under the steering column and see if the actuator moves when you switch from cold to hot. Also look at the linkage from it, is it also moving? If those are working but you are not feeling any temperature change on tat side it may be the door inside the housing has broken free and it stuck blocking the air. That may be what the previous owner meant as the only way to repair that door is to remove the dash and the HVAC housing so it can be taken apart to access the door. It would also explain why there are no codes as there is no sensor for the door itself, only the actuator.

There is no third blend door. The only temperature control doors for heat and AC are the left and right blend doors. Then you have the inlet air door, the mode door the two blend doors and the recirculate door. If the tech moved the blend door by hand but it didn't change the temperature it is likely the door inside the case has broken or the seals on it have failed. The heater core and AC core are shared parts for both sides. Air comes in through the inlet down into the HVAC case through the AC core then the heater core. There is where the blend doors work. Then out to the mode doors for defrost, dash, floor.

Yes it's a common problem, with it and it's brother the Edge and still is with the newer ones as well, the thing is that there are also multiple solutions depending on the failure. On the few I have done they have had a couple of bad actuators, two that were the plastic doors themselves. They had broken and the shaft just moved the broken part around. If it had been a vehicle I owned I would have tried a few "unauthorized by Ford" repairs to make the various parts more durable. Only one was repaired by doing the HVAC reset, and it only lasted about 2 weeks and failed again. I've also talked to folks who have unplugged and then reconnected the actuators and had things suddenly work again.
I do know of one person who got rather upset at Fords design and their response to the issue who removed the actuator and added a push pull cable for the drivers side blend door!

One thing you might try, get one of the cheap inspection cameras that connect to your phone and slide it into the case and watch the actual door movements while you actuate the system. That would tell you a lot.

If they had the system out to replace the heater core it may be the door was replaced at that time, but it's a real flimsy piece that has been known to break if you hit a pothole. Hard to know for sure without all of the paperwork. The heater core feeds both sides so if you have the same poor heat on both sides or get a P0128 check the thermostat or core. Unless they neglected coolant service or added sealer for? Reason the cores usually are not the issue.

Correct, it is a blend door that isn't moving. That is the only item that only effects one side of the system. The mode door is split but if it failed you would have the air coming out in odd places like the dash vents on the drivers side and the defroster on the passenger. The others control the air source, either through the fresh air intake under the cowl or the recirculate door behind the dash but you could have a internal blend door ht is broken inside the HVAC plenum.