If it's an ad hoc hypothesis overall, or if they know part of it; that co2 build-up faster in alveoli, and if so if they know it has an effect on the arterial CO2 tension.
In this study maximal breath hold duration on full lungs was 150s and it decreased to 90s when lungs were filled to 60% of the vital capacity. However, even though apnea duration was much shorter at 60% VC, the amount of CO2 in the end tidal air (which is considered to have the same composition as the alveolar air) was the same as after breath hold on full lungs (actually it was even higher but the difference was not statistically significant). pCO2 in the alveolar air and in the arterial blood is virtually the same (please don't ask me if it's only my assumption, it's basic physiology). Therefore, the conclusion is that CO2 level in the arterial blood rises much more quickly when the volume of air in the lungs during apnea is low.
the reason it dosen't makes sense is, that it is not explained why faster build-up of CO2 in the alveoli at the small lung volume, will lead to a more rapidly rising arterial CO2 tension
This is because normally CO2 diffusion in lungs is complete and partial pressure of CO2 in the alveolar air and in the blood flowing through the alveolar capillaries equilibrates. So if pCO2 in the alveoli increases it must increase also in the arterial blood.
"So while the full lungs contain around half of the O2, they can only buffer a tiny fraction of the total CO2. It means that when you decrease the lung/blood ratio by exhaling, the buffering capacity does not change much O2 storage and CO2 storage."/Trux
This is true if you consider total body CO2 content. The amount of CO2 in lungs is very small compared to the amount in blood. However, blood also contains only a small fraction of total body CO2 content, much more CO2 is dissolved in tissues. Nevertheless, although lungs do not contribute much to total body CO2 content, the level of CO2 in lungs is of the greatest importance. This is because it determines the level of CO2 in the arterial blood. And this is what is really important in terms of initiation of contractions and diving reflex. This is because both central and peripheral chemoreceptors "sense" CO2 level in the arterial blood. CO2 is the most important factor responsible for the urge to breath, this is because chemoreceptors are much more sensitive to a rise in CO2 level than drop in O2 (it has to fall below ~60 mmHg).
I'm not sure what was the context of the quoted statements by Trux and Eric Fattah. Maybe they were discussing FRC diving. I'm talking about static breath hold. I can't find any reason why arterial CO2 level during static breath hold on empty lungs would rise at a lower rate than on full lungs.
Another thing: Do we really know where the body measure co2-levels in relation to DR?
Yes we do. CO2 level is detected by arterial chemoreceptors (found in the carotid arteries and aorta) and by central chemoreceptors (in the brain stem). Both are important for initiation of the diving reflex. There is also some data indicating that diaphragm may be able to detect changes in blood CO2 level as well. However, it is not well proven.