Using Red Hat Docker image as base image I am considering using https://access.redhat.com/containers/#/registry.access.redhat.com/rhel7 as a base image for my Dockerfile instead of getting some random image in DockerHub. The main reason is the vetting process the images undergo.

Once any additional dependencies are installed, the resulting image will be pushed to a private Docker Hub repository. Is this a valid process or is there a disadvantage that I've missed?
As long as you have access to the FROM image registry, you are totally free to choose where to pull from and where to push to.