Could you cite the state law that supports your assertion? I should warn you that it will be difficult for you to do since Mississippi does not have party registration and voters are free to vote in whichever primary they choose. What is not permitted is to vote in a Republican Party runoff when you have already voted in the Democrat Party primary.
Besides, why shouldn't they vote for Cochran? He is the Democrat candidate and if reelected will continue to be the Democrat Senator from Mississippi. What is shocking is the number of Republicans who voted for this guy in the Primary and who will vote for him again in the runoff after he and the Democrats have shown his true colors.
MS Code 23-15-575, states: “No person shall be eligible to participate in any primary election unless he intends to support the nominations made in which he participates.”