Yes in some cases there is also the 'grass is greener' thing going on.While I am sure that some of them want to get to know their other parent better, its far more likely that its more of a "grass is greener" mentality with a lot of teens. Many of them spend mostly quality time with that parent, so then assume that living with them will be like that all the time...particularly if they are rebelling against the rules and discipline being maintained at the custodial parent's home.
Its also not uncommon for some teens to gravitate towards the same sex parent.
However, unless the custodial parent agrees, its not going to happen without a trip to court, and judges react very badly to parents who try to keep the kids after summer visitation. Several members here can attest to that, first hand.
In this case, there are no court documents making either of them the custodial parents. The parents are still married. So both parents have equal rights to the child.