Fat Oxidation rates can be increased through training. This was demonstrated in this study (Hetlelid KJ, Plews DJ, Herold E, Paul B Laursen, Stephen Seiler. Rethinking the role of fat oxidation: substrate utilisation during high-intensity interval training in well-trained and recreationally trained runners. BMJ Open Sport & Exercise Medicine 2015.). The study compared well trained (WT) to recreationally trained (WT) athletes on the same HIIT test. Both groups had similar carbohydrate oxidation rates but the WT athletes oxidized substantially more fat than the RT athletes.
Fat oxidation (0.64±0.13 vs 0.22±0.16 g/min for WT and RT, respectively) accounted for 33±6% of the total energy expenditure in WT vs 16±6% in RT most likely very large difference in fat oxidation (ES 90% CL=1.74±0.83) runners.
Despite similar RPE, blood lactate and carbohydrate oxidation rates, the better performance by the WT group was explained by their nearly threefold higher rates of fat oxidation at high intensity.
Note that this was not comparing Low Carb to High Carb athletes but it does offer the possibility that increased fat oxidation can lead to an increase in performance.
2018-07-08 Update: Found this interview with one of the study authors (Paul Laursen, PhD, and Dr. Phil Maffetone: Rethinking The Role of Fat Oxidation At High Intensities, Plus Practical Diet and Training Applications To Yield Results and More).
I don’t think this study invalidates anything related to RER and the VO2max testing. The FASTER study curves shows that some athletes (low carb ones in particular) are better at burning fat at higher intensities.
This does reinforce the value of training to increase fat oxidation rates. Increased volume is only possible through longer training which is done at a lower heart rate.