There is a discernable difference there, between 殴られる謂れはない and 殴られてやる謂れはない.
When you say 殴られる, you are making a statement matter-of-factly. When you say 殴られてやる, you are stating intent, making clear that your own volition and agency are involved: you are actively allowing 殴られる to happen. Also やる is crude あげる, serving to lifting the speaker's own position. 殴られてやる: I let you beat me up as a favor. I will go easy on you.
There's no reason/it's unwarranted for me to get beat up.
(Okay fine, but 1. maybe nobody wants to beat you up; 2. maybe it's not up to you)
There's no reason/it's unwarranted for me to let people beat me up.
(I am hereby announcing my own intention which is I won't allow myself to get beat up and I will take action accordingly)
And that's why the character then says おれは手加減はしない (I'm not gonna go easy on you/I'm not holding back/I'm not pulling any punches)
It's like in English how people say, "I'm not going to sit here and have my name tarnished by detractors."
By the same token, 振られてやる means "I am going to let you (someone else) break up with me." "I am allowing that to happen."
I will let you dump me/ I will let you dump me/ Cuz I don't wanna be in the way