If that was the case then the Cards would have had Butler as their DC several years ago.
I looked it up and it appears you are right, (according to a website that may more may not be legitimate but I think it its). There are only two tiers of coaches, head coaches and assistant coaches. Coordinators and assistant head coaching titles do not matter.
Apparently, these guys represent a lot of coaches despite the horrible website they have, which breaks one of my most hated writing peeves.
"We have negotiated with literally all 32 NFL teams"
LITERALLY IS NOT A NECCESSARY WORD! It makes them sound like 14 year olds wrote the website.
Anyway, here are, like, literally all the rules they have on their website. Literally.
http://www.prostarcoaching.net/library/NFL_Contact_Rules.pdf