All the listed statements are true regarding the Homestead Act, but if we had to identify the one that's typically misinterpreted, it might be option a. While the Homestead Act did allow women to file for land, the social and legal context of the time often made it more difficult for women to actually claim and retain that land compared to men.
Thus, the correct answer, indicating what is commonly misunderstood, is: a. Women were allowed to participate and received ownership of land.
This statement can be misleading because, while women could claim land, in practice, many faced significant obstacles and social barriers in doing so.