First, whether or not you can do a parametric test depends on which test you are wanting to do and what form of non-normality your data takes. Some tests handle some forms of non-normality better.
Secondly, and I am not speaking from book knowledge here, but trying to apply logic. It would seem that if a population is seen to be normal (which, FYI, hardly ever exists unless it is based on a standard score) and the sample which you have is not normal, that you indeed have a sample that differs from the population. I would think that is absolutely possible. Just because a coinflip is 50% doesn't mean that in 20 flips you will have 10 heads and 10 tails. In a million you might have a 50/50 split though.