During the interview, Branham said: "I think there is a group of magistrates that have a personal vendetta against my office staff."
He added later that "I think they are organized, and it's pretty obvious to me that they are meeting before Fiscal Court meetings."
The pay for Elswick and Wills has became the subject of some disagreement after they left the office last year during the campaign season and were rehired by Branham in January.
But McCord and Smith both took issue with the comment Wednesday.
"When I talked to you, I explained my feelings on everything right," McCord asked Branham. "I just didn't particularly like that comment that was in the paper."
Smith explained that some magistrates do talk to each other in accordance with the law, but he said they do not hold illegal meetings.
"I don't do that, and I don't think any of the others do," he said.
Branham agreed that talking on the telephone, meeting one-on-one or with two or three officials at a time does not violate the law. But he said he did not describe any actions as illegal in his comment.
"The insinuation of illegal, I never meant it that way. I would never insinuate that someone was doing something illegal," he said.
Under state law, magistrates are prohibited from meeting in groups large enough to constitute a quorum without calling a formal meeting. Groups smaller than a quorum are not subject to the same restrictions.
Sixth District Magistrate Bonnie Hummel also took a moment to address the public over her vote on the budget, noting that she personally spent hours reviewing it.
She said she supported moving $100,000 from the outlay account into a new line item for possible changes to the county's planning and zoning policy, because it was recommended by the committee chairman.
Hummel added that she also had supported Branham's recommendations for staff raises even though she did approve the overall budget after magistrates denied Branham's request.
"There's a lot of homework that we do that people don't know (about), and we put a lot of effort into it before we cast our votes," she said.