That’s NOT an Earth-based explanation. In the scenario you propose, the 4-minute lag would still be seen by an observer in Earth-orbit who measured the gamma rays themselves (which the researchers didn’t do.) [Your initial objection was “...there are atmosperic interactions here. To verify this 4 minute delay you need space based gamma ray telescopes free from atmospheric effects.”]
But it IS an interesting attempt to explain how the 4-minute lag could be created somewhere between Earth and the blazar.
Yes, upon calm/occam razor reflection, it seems most logical that the 4 minute delay of gamma rays vs radio waves is produced right there in the head of the blazar, not in our atmosphere. It then is just a matter of the right geometry, convex or concave head/wave front. We know gamma rays are emitted by accretion discs, sudden collisions like the 20 fragment SL9 comet train impacting Jupiter, etc. Thus it boils down to how that gamma ray producing region lags some .5 AU behind the radio wave region...geometry...new theories not needed.