Those studies show the birds taking a large variety of flying insects, most of them considerably larger than a mosquito. Those studies also show very few mosquitoes in the diet. There are some reasons why mosquitoes should typically make up only a small part of a martin's diet. First, mosquitoes are primarily nocturnal. Not exclusively, but primarily.
Martins are primarily diurnal.
Martins and mosquitoes are both active at dusk and dawn, and undoubtedly the birds take some of the little pests, just as they take almost everything that flies. But if you live where there are a lot of mosquitoes, you know that the real agony starts when the sun goes down. The fact is that mosquitoes offer virtually no nutritional benefit, certainly not enough to make it worth the martin's time to actively pursue them as a primary item in the diet. I do not doubt that martins will scoop up one if they come across it during their foraging, but imagine how much energy it would take to catch enough to feed not only themselves, but their young as well. It does not make biological sense.