Yes, a parent can have impostor syndrome. I would imagine most parents think their kids are fairly normal, or if gifted, "suitably" mildly gifted. Let's look at your concerns:
1. WPPSI/pscyhologist. I have heard that scores could skew a bit high on WPPSI III. DYS program required a higher score than for other IQ tests on the WPPSI III. Which test did your child take? Unless you received notice that your particular test was invalid, I wouldn't be too concerned re: pyschologist unless you have many other reasons to doubt the scores.
2. Traditionally gifted characteristics. If you have seen one EG kid, you have seen one EG kid. Everyone is different. I happen to have a pretty lazy kid, who learned early on how to do the least amount of work to get a good-enough grade on projects. He doesn't love school. His biggest GT thing, I think, is not something that is super out there -- he has the ability to understand pretty much anything. His current motivations are all computer-related. My kid also likes to hide his abilities, and we have had to stay on top of things to make sure he is getting challenged/learning new material.
3. Stay at home parent/teacher is likely to be GT as well, and thus doesn't notice that child is different.
How is the curriculum? Is it too hard/too easy/OK? If the teachers were surprised by the MAP scores (another indication of GTness), I'm wondering if there is a chance that your child may be underchallenged? Something to think about.
If you are unhappy about the school setting, are there other options?