This is pretty spot on. I'm from Illinois and when I went to NXN Nike basically said, "hey we're calling your team xyz, is that okay?" We said "sure", but no idea if we could've changed it or anything. I'm assuming there are lots of other schools that fall into this category.
You're correct, in IL coaches are not allowed to attend, even if they use their own personal time/money. FWIW I know some coaches don't follow this rule and just so happen to appear at the race, but it's against the rules.
Interestingly Illinois has no restriction in terms of the gear/apparel/all of that. I remember when I went the teams from Indiana had to choose whether they wanted to keep the backpack or the sweatshirts or the other gear. I think they were limited to like $80 worth of gear or something. Then there are the teams from other states that somehow walk away with multiple singlets and multiple pairs of spikes.