Given the wide-ranging achievement scores, I would wonder if his WISC-V was similarly divergent, at both the index and subtest levels. If the psychologists you've spoken to are working with all of the information you've given us, I'm slightly surprised at their conclusions. (But not entirely so.) Max'ing out the WIAT-III math composite is completely incompatible with being average in intelligence, the WISC-V FSIQ notwithstanding.
I should point out that the SBAC language measures are not fully equivalent to producing organized or lengthy written language in class, especially on topics of no personal relevance. Being able to recognize correct/incorrect grammar/usage/mechanics is not the same as being able to produce it in open responses, while composing original language. Also, the open responses on the SBAC are typed, which may accommodate certain kinds of writing disabilities sufficiently to allow fuller expression of one's underlying expressive language ability. Finally, some learners find test-taking to be a fun and motivating challenge, more so than daily work.
