Both DH and I have health insurance plans with good coverage. Each cover any psychological service up to a maximum of $750 per person per year. DD's initial testing in grade 2 was completely covered. All receipts were made out as 'psychological services' and for the parts of the psych ed where the parents were included, like the initial interview and results appointment, the receipts were provided in DH and my names. Between the three of us and double coverage, everything was covered. When DD was retested this year for dyslexia, it was again 100% covered. We are in Canada and I am not at all sure how our insurance plans differ from those in the U.S.
When my nephew had his psych ed, my sister's coverage was less than stellar so she scheduled the assessment in December/January so that she could bill to two different calendar years and maximize their coverage.