You don't have to be "nominated", anyone can apply even if they weren't nominated.
People to People has been investigated in the past for using mailing lists for their nominations. They sent a "Congratulations, you've been nominated based on your excellent achievements" letter to the name of a child who died in infancy. After that they were supposed to fix their marketing practices. You can google for further info if you like.
I do know kids who went on PTP trips, and they enjoyed them. But I don't like that the company presents it as a big honor when it isn't. I also don't like the whole sponsorship/begging aspect.
I have no doubt that kids have a great time on these trips, but they are not an honor, and are more expensive than if you booked a trip yourself. I'd rather take my kids overseas as a family, and it would be just as educational.