Well, if they were well positioned, like Hatshepsut, they used their brains to gain power. Catherine the great was another great strategist.

If they were impoverished, wouldn't they have just made a bad situation better? Relatively, they wouldn't have become a scholar, but maybe created methods to provide and build on a family business?

Lucretia borgia even made pope. I just looked up brilliant women in medieval times and got an interesting list.

http://www.toptenz.net/top-10-plus-1-ladies-of-the-european-middle-ages.php

There are and have always been outliers.