Yes, in a legal sense, Red Hat owns most of the infrastructure, the trademarks, and signing keys, etc. Nevertheless, most of what happens in Fedora happens because people volunteer their time (both Red Hat employees and contributors), and there is no control over that, it depends mostly on the good will and engagement of volunteers.
Fedora can and does make independent technical choices. Some examples were mentioned upthread. Nevertheless, Fedora is not independent. In particular, Fedora is not allowed to create legal jeopardy for Red Hat, so it is very strict on USA copyright, patent laws, export controls, etc. Red Hat funds Fedora because it is useful for the company by driving the development of the Linux ecosystem and technologies that will form the basis of subsequent versions of its enterprise offerings. If Fedora were to go in a completely crazy direction, it’s likely that Red Hat would stop seeing this benefit and pull its involvement. It would be very hard for the community to keep Fedora working without that support. So Fedora’s independence certainly has limits.
Nobody has full control. The Fedora Project Leader can try to convince contributors, but has no power to direct work. Red Hat lawyers set some strict limits based on relevant laws, but that just sets some boundaries. Contributors decide what they want to work on and when. Various committees like FESCo and FPC “govern” by consensus and voluntary conformance. Red Hat employees working on Fedora to a large extent do this on their own, so their contributions are not controlled by anyone. Some people are paid to work on infrastructure, but there is more to do do than the resources permit, so they make some semi-independent decisions what services to keep working. I would say that this is all rather complicated, and getting things done is mostly possible when there’s general support for something, and that is how it should be.