Fuck no...
dumb kid at a good school Vs. a reasonably smart kid at a dumb school.
People often draw their motivation and from the atmosphere around them this is why at selective schools the kids do so well, not only because they are smart but because of the mentality of the student body as a whole. You also have the whole class doing well which pushes up your marks. I don't know about the rest of you, but i personally don't feel much of a sense of accomplishment when I do really well against people who are obviously not as good as me at something.
If you are in an environment that presents inferior opportunities in comparison to your potential, you are likely to grow complacent about your academic superiority in relation to your cohort thus developing a stagnant academic lifestyle. Perfection is a myth, it does not exist within human beings, in thinking that we are perfect we only move further away from any hope of ever truly attaining it. Conversely if you are in a more academically competitive environment you would be more inclined to strive to remain ahead of (or keep up with) of those around you.