Reason(s) for the school to pay for IQ testing:
-- to determine placement
-- parents prefer not to pay for it themselves
(ask yourself how likely they are to want a high-cost alternative to achievement testing, and then ask yourself what impetus they have to seek accurate information if everyone suspects that the child might be HG+, maybe even way beyond HG.)
Reasons for YOU to pay for it instead:
-- YOU control who sees the information
-- YOU get the full report
-- YOU choose who does the assessment
-- YOU choose what tool the evaluator will use
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Honestly, those are pretty compelling reasons for outside evaluation. Assuming that you need it to begin with, of course.