Exercise helps, but the evidence for it is mixed. I don't think there's any amount of exercise you can do to undo the damage of a toxic diet, which the standard diet tends to be.
And as proof there are professional athletes that end up suffering from chronic illness and inflammation. Even more so, intense training like for running marathons can make you sick, because it can lead to a suppression of the immune system due to the stress involved . On a cursory search I found a meta-analysis on studies on the effects of marathon running on inflammation markers and the results are very mixed, endurance running promoting both anti- and pro- inflammatory markers. 
Therefore your claim doesn't stand to scrutiny, even though we can agree that exercise is mandatory for being healthy in general.
> "Justifying meat consumption with a tribal population that often runs marathons to catch said meat is baffling to me."
In your original comment you pointed at a population-level study (your second link). Why is mentioning a study on an indigenous population any less valid? Is that a double standard I'm sensing?
We study indigenous populations because chronic diseases are very modern and it has something to do with the modern environment, which includes the diet, especially since many of these populations got sick after being transitioned to the western diet.
The Masai might have been exercising more and live with less stress, which might have contributed to their overall health, or maybe they ate that meat with something else that reduced the inflammation, however this is an admission that context matters and that reductionist statements such as "red meat is inflammatory" are wrong.
Also apparently we burn as many calories as hunter gatherers , so I would be careful about such statements.
> "From my studies on ancestral human eating patterns, it seems that most were almost entirely vegetarian, and may have only eaten meat during celebrations a few times in a year."
The article you linked to is entirely devoid of any tangible proof and given the editorial style I can't take it seriously.
Indeed, the diet of apes and monkeys is composed of leaves, nuts, fruits and insects. However this is a very bizarre argument. Us becoming omnivores and starting to hunt animals and eat meat is what allowed us to adapt to harsher environments and to grow our big brains. Eating meat is what made us human and what drove us to develop tools made of stone for hunting or for collecting the bone marrow, it's what drove us to use fire for cooking, in order to increase the bio-availability of the meat and the starches that we eat.
First of all because our big brain can only be explained by the availability of high-calorie foods. High-calorie foods are not very available in nature in edible form. We couldn't have digested many of the high-calorie starchy plants that were available. The prevailing theory is that fire was first used for cooking in order to cook starchy plants that were toxic otherwise. But the first known use of fire was only 1 million years ago  and does not coincide with the expansion of our brains.
Use of stone tools however coincides with the expansion of our brains, yet routine use of fire may have began only 300,000 years ago , which means starchy plants weren't very available for us to eat, certainly not enough to explain our high-caloric diet.
The best indications for what our ancestors ate comes from looking at modern hunter-gatherers and we've got plenty of such populations observed .
Observed hunter-gatherers obtain most of their energy from animal foods . From the groups studied in that reference, they found ...
- 46 groups that obtained 85% of their energy from meat, fish and eggs (with no groups obtaining this much energy from plants)
- 133 groups that obtained 65% of their energy from meat, fish and eggs (only 8 groups that obtained 65% of their energy from plants)
- the median average obtained 70% of their energy from animal sources, 30% from plants
Note that this report has been criticized to have some flaws, but there is a substantial body of evidence for the theory that, on average, hunter-gatherers got 70% of energy from animals   .
 Cordain, L. “Implications of Plio-Pleistocene Hominin Diets for Modern Humans,” pp 363-383 in Peter S. Ungar, ed., Evolution of the human diet: the known, the unknown, and the unknowable, New York: Oxford University Press, 2006.