Florida’s Republican Gov. Rick Scott says he’s concerned about the privacy safeguards on information shared with the health-care law’s “navigators.” (J. Pat Carter/AP.)

(Update 10/8/2013: Tennessee settled and agreed to narrow the scope of its rules.)

Enrollment in the president’s health-care law began Tuesday, and some local governments are fighting their states over the right to explain it to their residents.

The fights in at least two states — Tennessee and Florida — revolve around the law’s so-called navigators, people hired to explain the intricacies of the law and the options available. State lawmakers say they’re concerned about the privacy of those being advised. The local governments say those concerns have been addressed or are overblown, and they just want their citizens educated on the insurance options.

In Tennessee, the state’s Department of Commerce and Insurance recently issued an emergency rule requiring navigators register with the state, get fingerprinted and pass a background check.

In a filing, the state argued it was meant to “to ensure that individuals who are not of good moral character cannot act as navigators” and to protect citizen privacy. But advocates with the League of Women Voters and the Tennessee Justice Center sued the state over the rules on Friday. And the city of Nashville joined soon after, the Tennessean reported.

“[T]he State’s emergency regulations are so over-broad and vague that they affect the ability of the Metropolitan Government to fulfill is [sic] government functions and provide information to its citizens,” Saul Solomon, the director of law for Nashville told the paper. The rules inhibit librarians and health officials from serving the public, the city argued.

The Tennessee rule prohibits navigators from discussing “the benefits, terms, and features of a particular health plan over any other health plans.” That, the advocates and Nashville say, infringes on their First Amendment rights.

Meanwhile, Florida’s Republican Gov. Rick Scott has repeatedly complained about what he describes as insufficient privacy safeguards on the information navigators collect, leading his health department to ban navigators on state grounds.

“Floridians should not have to exchange their privacy for insurance,” he wrote in a letter to House Speaker John Boehner (R-Ohio), and Senate Majority Leader Harry Reid (D-Nev.).

At least two Democratic counties — Broward and Pinellas — have figured out a way around the ban: allow navigators on county property.

“The people of Broward County should have access to healthcare and we are capable of making informed decisions about our own healthcare options, we can make up our own minds,” Broward Mayor Kristin Jacobs said in a statement after the Broward County Commission voted 8 to 1 to allow navigators in county facilities. Pinellas County is planning a similar arrangement.