LA Revised Statutes 42:19 —

A public body may hold an executive session pursuant to R.S. 42:16 for one or more of the following reasons:

(1) Discussion of the character, professional competence, or physical or mental health of a person, provided that such person is notified in writing at least twenty-four hours, exclusive of Saturdays, Sundays, and legal holidays, before the scheduled time contained in the notice of the meeting at which such executive session is to take place and that such person may require that such discussion be held at an open meeting. However, nothing in this Paragraph shall permit an executive session for discussion of the appointment of a person to a public body or, except as provided in R.S. 39:1593(C)(2)(c), for discussing the award of a public contract. In cases of extraordinary emergency, written notice to such person shall not be required; however, the public body shall give such notice as it deems appropriate and circumstances permit.

(2) Strategy sessions or negotiations with respect to collective bargaining, prospective litigation after formal written demand, or litigation when an open meeting would have a detrimental effect on the bargaining or litigating position of the public body.

(3) Discussion regarding the report, development, or course of action regarding security personnel, plans, or devices, including discussions concerning cybersecurity plans, financial security procedures, and assessment and implementation of any such plans or procedures.

(4) Investigative proceedings regarding allegations of misconduct.

(5) Cases of extraordinary emergency, which shall be limited to natural disaster, threat of epidemic, civil disturbances, suppression of insurrections, the repelling of invasions, or other matters of similar magnitude.

RS 42:17 —

Upon unanimous approval of the members present at a meeting of a public body, the public body may take up a matter not on the agenda. 

Any such matter shall be identified in the motion to take up the matter not on the agenda with reasonable specificity, including the purpose for the addition to the agenda, and entered into the minutes of the meeting.

Prior to any vote on the motion to take up a matter not on the agenda by the public body, there shall be an

opportunity for public comment on any such motion in accordance with R.S. 42:14 or 15.

The public body shall not use its authority to take up a matter not on the agenda as a subterfuge to defeat the purposes of this Chapter.

Media reports do not indicate whether Rapides Parish police jurors added the ambulance provider question to their agenda Monday or took it up under another item. Discussion in executive session took about an hour.

Which permissible category for closed talks ambulance service offers fall under is unclear. 

Draw your own conclusions.