They only have to admin the DNSSEC stuff (publish your domain name keys along with your nameservers, as you set them up through your regular domain provider).
The DANE part needs no further support than you being able to use DNSSEC for your domain's DNS. Obviously there is always some entity controling each TLD, and that entity can screw up your domain if it acts improperly.
You're not following. DNSSEC is secured by a chain of keys leading to a root; the entity that controls the root controls the chain. If you use DNSSEC to authenticate your certificate, you're giving control over your certificate to whoever runs the roots.
Nobody is suggesting that the naive X.509 scenario we had a year ago is secure. They are, however, skeptical of the idea that we should invest millions of dollars into an architectural change to the core of the Internet to land... right back where we are now.
The DANE part needs no further support than you being able to use DNSSEC for your domain's DNS. Obviously there is always some entity controling each TLD, and that entity can screw up your domain if it acts improperly.