That's basically it, while chicken pox infection along with occasional contact with infected individuals provides very good life long immunity the vaccine doesn't.

Are there studies backing the latter? Seems like it could only be speculation at this point,

The phenomenon is real. We know that chickenpox vaccination increases risk of shingles.

What is at debate is the morbidity of shingles and late life chicken pox + the cost of boosters offset by the reduction in total chicken pox? Not so clear.

Here is an unfavourable paper on the subject https://www.ncbi.nlm.nih.gov/pubmed/22659447?dopt=Abstract

Universal varicella vaccination has not proven to be cost-effective as increased HZ morbidity has disproportionately offset cost savings associated with reductions in varicella disease. Universal varicella vaccination has failed to provide long-term protection from VZV disease.

HZ = herpes zoster (shingles), VZV = varicella zoster virus (chicken pox)