Played 3 games now, and every time I play I get through the initial melee, and then get the "sorry, you don't have the killer..." message. Went through source, and it appears that it will happen every time. If the below is accurate, it looks like as long as you are 'rookie', you won't get a battle.
(scrShowPane gScreen "FirstFight")
(= arenaRank 'rookie)
(scrShowPane gScreen "NoMoreMelees")
(= arenaRank 'gladiator)