I'm of the opinion that this should ideally be his decision to make, but there are a number of other factors in play here, including his religious indoctrination and apparent ignorance of the nature of the treatment. I believe that public policy should reflect a youth right to self-determination, including medical consent.
In terms of the empirical literature's relation to such matters, I'd refer to Weithorn and Campbell's
The Competency of Children and Adolescents to Make Informed Treatment Decisions. Consider the abstract:
This study was a test for developmental differences in competency to make informed treatment decisions. 96 subjects, 24 (12 males and 12 females) at each of 4 age levels (9, 14, 18, and 21), were administered a measure developed to assess competency according to 4 legal standards. The measure included 4 hypothetical treatment dilemmas and a structured interview protocol. Overall, 14-year-olds did not differ from adults. 9-year-olds appeared less competent than adults with respect to their ability to reason about and understand the treatment information provided in the dilemmas. However, they did not differ from older subjects in their expression of reasonable preferences regarding treatment. It is concluded that the findings do not support the denial of the right of self-determination to adolescents in health-care situations on the basis of a presumption of incapacity. Further, children as young as 9 appear able to participate meaningfully in personal health-care decision making.
I'm inclined to believe that such empirical literature is suitable for general policy analysis, but not for evaluating specific cases such as this, obviously. It's true that he's been brainwashed, but IMO, all variety of religious fanatics are brainwashed to some extent. The most preferable course of action to prevent situations like this is to permit individuals of all ages to freely access the information that they wish to access, regardless of parental consent.