No. When you rent, you usually are paying (1) the owner's mortgage, (2) taxes, (3) maintenance and (4) profit. So renting the same place is almost always much more expensive than the mortgage payment.

Rents do not have to rise. They have been rising in most cities because people are moving to cities. Rents dropped in Detroit when a lot of people left. (Rents also rise with inflation.)

I do wonder about the data. It compares the median rental to the median house purchase. And people usually rent smaller places. So, renting is usually cheaper because of that. I don't know that it is an apples-to-apples comparison.