There is no doubt a measurement system like Dirac or other auto EQ has the capability to determine direct sound and reflected sound. I'm not sure if they do as it would add some time but in theory they should be capable. While it can measure it, it can't change the speaker's dispersion properties or the room properties. They can't fix many acoustic problems like SBIR (speaker boundary interference response).
The software we use at work (TEF based) it will show us where reflections are happening in a room. Trinnov with its 4 microphones can do something similar for its remapping. We can decide whether to treat that reflection and what type of treatment would work best. These auto EQ systems simply do not take enough measurements with just a few locations that a mic is placed. It basically does averaging with multiple locations with a weighting towards the primary listening location. But, they can determine the direct vs reflected sound if they choose.
In a nutshell they take a few measurements and try to take their best educated guess on what to EQ and what to leave alone. Sometimes it is a positive result other times it is not. Also, in a given room one EQ algorithm might do a better job than another. So while Dirac might technically be better it might not have better result in every room. In some rooms YPAO, Audyssey, ARC, Room Perfect, etc. might work better. We can measure 100 rooms and see which one gets improvement in most rooms but in a given room does mean it will be the best. Auto EQ is somewhat of a crapshoot.
People should not rely on EQ to get good sound. with acoustics we say good sound comes from location, location, location just like real estate. But with acoustics it is... location of seating, location of speakers/subs, location of acoustic treatments. Of course this assumes quality equipment including speakers and subs. If you have decent speakers and equipment, place everything well and do a proper set up, EQ will be the icing on the cake but it can't replace the cake.