Assert a plea of self-denfense

"Gentlemen of the jury, you have heard the facts of both sides. Mr. Brown had in his possession at the time one butcher knife, two razors, one set of brass knuckles, and a blackjack. Mr. Smith had on his person, one sickle, one hatchet, two meat saws, a cleaver, and an ice pick. Both men plead not guilty, each asserting a plea of self-defense. I judge you have reached a verdict." The judge said.
"We have, your honor."
"And that verdict..."
"We, the jury, would have cheerfully paid one dollar per man to have seen the fight."

Does "each asserting a plea of self-defense" mean " each stating firmly that their reason why they had a fight was to self-defend themselves"?