No, Tennessee is saying that the FCC doesn't have the authority to regulate how a state governs its towns -- and they are right, the FCC doesn't. Congress may pass a law, which is then voted upon and approved by the representatives of the people - but the FCC is an appointed body without the power to usurp the power of the states to regulate their own cities.
The FCC has the right to regulate interstate communication, but its right to regulate INTRA-state communication is rather limited. Being federal does not automatically make the more powerful, Unless it crosses a state line, they really don't have a leg to stand on.
That being said, from what I understand the issue is that Tennessee has established territories in which a municipal utility can operate. Presumably this territory was defined as being an un-served or under-served area some time in the past. What Chattanooga wants to do is provide services outside of its territory, which Tennessee has regulations to prevent.
What SHOULD happen is that Chattanooga should go the state regulators and ask them to designate the under-served areas as part of their territory, then they would be free to expand into it. Instead, they wanted to do an end-run around the laws and regulations under which they were created.
The other problem is that they are an POWER company trying to provide communication services. They should have instead established a separate utility.
I don't have a problem with municipalities establishing broadband networks. I get my own connection though one, and am VERY happy with they service I am getting. But they need to be done right.