No actually, it is too easy to say that the custodial parent is solely responsible- ideally, even if parents are separated, they are still both responsible for what their child does- they are both still the parents. It is too easy for the absent parent to simply reduce themselves to "fun" weekend parent and ignore the discipline problems which they also have a duty to tackle.
Having said that, I do not know the precise facts of this case- maybe the parents are not on speaking terms (sad, when there is a child involved), or they are not able to communicate about problems, or maybe the dad is a wassock, or maybe the mum makes it difficult for him to intervene, and makes pathetic excuses for her kid because she doesn't want to oppose her. This does not exonerate in any way the absent parent- you can go to family court as the non-custodial parent if you have any concerns that you cannot resolve amicably about the child's upbringing. It's just all too bloody easy otherwise: you find a new person, bugger off leaving old partner and kids, and become fun person in child's life without any responsibility. D'you think that could cause some discipline problems of its own?