There appear to be several questions here: appropriate frequency of retesting, reliability/validity of his original assessment, and how one accesses assessments with or without out-of-pocket cost.
The frequency of cognitive assessment depends on a couple of things, including the purpose of testing. At the most basic level, the same instrument should not be given more frequently than every 24 months--but of course, it's been long enough that this would not be a consideration.
One can always pay privately for an assessment (dependent on one's financial resources, obviously). Most major metropolitan areas have at least a handful of private practice evaluators who would be able to provide this service. Health insurance will only pay or partially-pay if there is a health-related concern. Your local educational authority (public school district) is similarly only obligated to offer an assessment if there is a specific concern--typically disability-related. (And even then, at limited frequency, since they can reference recent testing for disability-related evaluations, instead of duplicating it.) If the reason for retesting is principally his own curiosity, rather than to answer a question impacting his access to his education, then the district would be under no obligation to assess him.
Was his original testing reliable or valid? Most likely, but with general caveats. Assessments of young children are often not entirely stable (rule of thumb usually looks at assessments at or after about age 9 or so as more predictive of adult performance). And he is, of course, correct that he might not have demonstrated the full range of his skills, due to his small-child-perspective on the testing process. FWIW, one should also remember that extreme scores (very high or very low) tend to show greater regression to the mean on retesting, so a second assessment could well be substantially lower for that or other reasons. The RIAS is also known to read somewhat high compared to the Wechsler family of assessments, for reasons that are not entirely clear. And in this case, he took the test at an age when there was quite a bit of ceiling left to him (the test runs from preschool to adulthood), at an age where the absolute range of skills available on the test was much greater than what remains for him now as a middle adolescent. Even if he were to take a test that ranges up into adulthood, the distance between a highly capable teen and an NT age peer is much more difficult to distinguish than the distance between them in early elementary.
IOW, an entirely valid and reliable score now could be either higher or lower (by quite a bit) with complete legitimacy.
