Frontier was purchased about 9 months ago by a private equity group called Indigo Partners.
Indigo Partners is the same company who purchased Spirit Airlines several years ago. They transformed Spirit into what it is today and then sold Spirit to the general public via an Initial Public Offering (IPO). Indigo retained a large percentage of ownership in Spirit up until about 11 months ago when they sold their shares. It was basically a "fix-and-flip"--only with an airline.
The common assumption is that Indigo Partners will apply the same or a similar formula to Frontier Airlines. This probably explains why we're seeing an unbundling of services with separate pricing for everything they can think of.
So no, Spirit doesn't own Frontier.
One does not bear arms against a rabbit. -- Garry Wills