The weird thing to me, then, would be that they are using the WJ-III if they're wanting to see what her needs are in terms of current achievement. While it is an achievement test, it really doesn't line up well with the typical school curriculum and the grade equivalents (GEs) in particular can be rather screwy in young kids.
I just had dd14's old WJ-III scores from when she was a 2nd grader out (we're updating a bunch of school paperwork and we needed a long trail from the beginning of her testing) and she had GEs ranging from 4.4 to >18.0 on the entire thing save for two fluency sections (timed pieces, which have always been her downfall). Honestly, there is no way that she was performing at that level as a young 7 y/o, at least at the level of those upper end scores that were coming out in the high school+ range.
I, unfortunately, cannot say if the tester's experience will depress scores. Dd14 was tested by a grad student, but the grad student didn't have any reason to want to deflate scores so at least if there were mess-ups, they weren't intentional to reduce the scores.
I can see where you're worried, though, if they seem to be trying to come up with reasons not to enrich appropriately. Do you have any idea why that would be? I.e. - are they worried about setting a precedent with your dd where others start asking for more b/c she got it? Is she having a personality conflict with the math enrichment teacher? Something else?
