The info you're referring to is only true for N-fixing legumes, which includes clovers and beans, like soybeans -- NOT
grasses. So, N use will inhibit N-fixation in soybeans, which is why soybean fertility is different than turfgrass fertility.
You're jumping at a lot of non-lawn issues to prove the way you're doing your lawn apps. You linked how mycorrhizae can help in nursery crop production and in tree/shrub establishment on harsh sites and you've linked about how rhizobia interact with legumes, but you've linked nothing about how these impact lawns. Lawns surely don't benefit from N-fixing rhizobia, unless you are growing legumes in your lawns (which most people call weeds).
You guys are falling hook, line, and sinker for what the salesmen are telling you. You're totally ignoring the ecological differences between leguminous and non-leguminous cropping systems, as well as annual vs perennial cropping systems.