Seems to me if you're about to turn base and you know another aircraft's on final, in normal circumstances you won't reach final for about another minute, by which time the other aircraft will be a mile or so further down final. So you could only conflict if he was two or more miles out when you became aware of him.
Whether AG or AFIS, that aircraft should have been informed about other circuit traffic when he called for join, and if he was told the circuit's active, should have done an overhead join.
People joining straight-in when they either don't listen or don't care about other traffic are being very selfish as well as dangerous.