"Aging in place" is commonly defined as "the ability to live in one’s home and community safely, independently, and comfortably, regardless of age, income, or ability level."
Your parents who want to age in place probably define this trend differently. They simply want to remain in the place where they are comfortable, where they’ve lived for a long time and plan on living a lot longer. Not to mention they want to stay in a house that may be largely paid off and thus, is very affordable. Ultimately, they want to stay home.