Yes, this is what I saw asagle doing which does give you the right to seek revenge against them only once. Once you killed them for revenge, you cannot seek the player to kill them again unless they did something to you after you killed them for revenge. In the following screenshots, you killed them three times in a span of 3 minutes and 28 minutes if my math is correct.
When you killed asagle near the Ammunation in Commerce, you and [RA]GenSprite then drove to LS County Hopstial where asagle respawn. You both then chased asagle and killed them again near Idlewood or Gaton. What reason did either you or [RA]GenSprite have to purse and kill them them again?