A four year BSN program is a path to an RN, not "better than an RN". A BSN is a degree, an RN is a license you receive from the state.
The PP is correct. There is no such thing as a pediatric oncology nursing program. You complete nursing school
, pass NCLEX and then apply for jobs. With experience, there is a pediatric oncology certification exam you could take (CPON) but it is only possible to do this after obtaining pediatric oncology nursing experience. If you want to work in a specialty area, you're much better off getting your BSN as more and more hospitals (and especially the larger ones that have specialties like pediatric oncology) are beginning to demand them.
A PCT position is quite similar to a CNA position in my state. None of the large academic hospitals in my city called their aides "CNAs"... they were PCAs, PCTs, Clinical Assistants, etc. because these hospitals did not always require CNA certification to work in these roles.