(though it's likely I was and still am misunderstanding him - you'll see he gets a little impatient with me at one point).
He's like that! The guy is a software and math genius, and understands his field amazingly. But like most geniuses, he can be a bit short with the rest of us average Joe's! He tends to explain things in rather brief, terse and sometimes technical jargon, and assumes that everyone else should just get it, without question.
John seemed to imply that attempting to balance the sound from the speakers post-reflections/absorption would be detrimental
As Glenn mentioned, the issue is to FIRST balance the room acoustically as well as possible, eliminating all early reflections, or at least reducing them greatly in amplitude. Then, once the room is properly treated acoustically, that's the point where you can think about digital tuning.
I suspect that the point John was trying to make is that you cannot EQ a reflection, and trying to do so will create other issues that you might not even be aware of, except to note that the room just sounds "off" in some sense that you can't quite put your finger on. Reflections create phase issues, such as nulls or peaks in the response. You might be able to reduce the peak, but you cannot "fill in" a null. If you attempt to boost the frequency where the null is by applying an EQ filter boost to it, you probably won't actually raise it at all (since you are pumping more energy into the direct wave, but also the same amount of "more energy" into the reflected wave, so they still cancel each other out). Even worse, you run the risk of causing the unstable combination of reflection plus filter to "ring": the extra energy you are applying in the frequency domain, also has consequences in the time domain, as Glenn pointed out. The same applies to applying a cut to the frequency where a reflection null occurs: the combination of reflection plus filter can be unstable, and cause "ringing".
Here's a practical case, that explains it in simple REW graphs. I'm in the process of doing some digital tuning on a client's room right now, so I did just that (applying a filter where it shouldn't be), and here is the result, in the time domain:
There's a peak there at around 64 Hz, and one might think that a small tight PEQ filter right there would get rid of it, and in the frequency domain, that is true! You can actually "knock down" the peak, as you can see below:
If that's all you look at, the frequency response curve, then you think you did a great job, because you flattened out the peak! But that's only the
frequency domain. Now look what happened in the
time domain: Before applying the filter...
And after applying the filter...
Ooops! There's some nasty ringing going on now, because the unstable combination was triggered! Now, by carefully adjusting that filter in ways I'm not going into here, you can actually get rid of both the peak AND the ringing, like this:
That was possible in this specific case, because the room is already well treated, but that isn't usually the case. And here we are talking about bringing down a peak, which sometimes is possible, but trying to "fill in a dip" is an entirely different matter. Dips are phase problems, and should be dealt with using acoustic treatment, not EQ.
So, I'm guessing that's what John was talking about, in his cryptic way: trying to use EQ to fix reflections is a fool's errand. They should be fixed with treatment. EQ is the wrong tool for the job... sort of like trying to put in a nail using a screwdriver, or put in a screw using a hammer!

It's important to use the right tool for the right job. Deal with reflections in the initial room design an in the treatment. Deal with pure SPL issues using EQ.
As Glenn so rightly pointed out, EQ can ONLY be used successfully on a room that has FIRST been properly treated, acoustically, leaving only problems that can be fixed electronically.
So, the way you get symmetry in a room, which is critical for a control room, is firstly by balancing the layout of the room, and the treatment of the room, such that the speaker response is also already balanced (in other words, acoustic loading on the speakers is about the same, and the path taken by sound coming out of one speaker is a mirror image of the path taken by sound from the other speaker). And when that is achieved, with good overall acoustic response n the room, then you can use digital tuning as the "cherry on the cake".
That's the general process, but in practice, tuning a room is nowhere near as easy as it looks! And certainly is nothing like the marketing hype you seen on the glossy advertising for "room correction" hardware and software.
- Stuart