I simply don't see that there is anything mysterious or at odds "...with the mainstream physical understanding of atmospheric composition and the radiative transfer theories that handle these aspects of reaction in the predominant AOGCMs in modern application." I haven't fully read much less processed the actual paper yet, just a very cursory skim so far, I'll get back you after I've had the opportunity to fully read and review the paper, its data/processes, and its findings.
You haven't read it yet, but you don't see anything inconsistent. Let me help you...
My actual words are listed above, and while they don't appear to need translation to me, they are different in meaning than your paraphrase of my intent.
I see no compelling support for the assertions of the author in the data or described technique of data analysis. I see nothing that compellingly challenges mainstream climate science understandings or the physics of atmospheric radiation transfer. I see unfounded speculation based upon incomplete incidental data rather than the types of data required to produce a valid and complete TI assessment (the simplistic peak-trough measurements for TI work fine when you are trying to figure out the thermal inertia of a block of concrete, but the process is a bit different when we are talking about trying to measure the TI of a turbulent block of sky, where the mass of air you are measuring is not the same mass of air at mid-afternoon (~high temp.) and pre-dawn (low temp), there seem to be several inappropriate misapplications of standard theory, processes and modelling, but I've only made it through my first good solid read of the "paper." I use quotes there because technically this really isn't in the form of research paper beyond some sectional layout similarities, and I guess since it wasn't intended to be a science research paper, there is nothing wrong with that, but in its current form I'd be very surprised if it ever made it beyond editorial review yet alone preliminary peer-review in any professional science journal.
...That latter part .... "...it may be that the effective excitation bands bandwidth are SO NARROW that there is no appreciable energy retained." This couples with my OTHER LISTED skeptical concern about what we know in terms of Solar spectrum and trends in shifts of important spectral lines. We've only had access to accurate measurements of this for about 30 years as I'm about to explain to my buddy and pal OopyDoo when we chat about the width and placement of absorption bands in GH gasses.
It is indeed an oft repeated trope among the pseudoscience cranks, but it simply isn't an accurate portrayal of what extensive observation and experiementation over the last 150 years or so have demonstrated.