Gabriel could not bring Claire to a hospital. There are eyes and ears everywhere, and this could easily get blown out of proportion. He couldn't risk it. Yet, he also couldn't risk Claire's well-being, so on the way to the Residence, he has already called up Lopez the butler, who in turn contacted the best doctor they know.
Lopez has also arranged everything in the Residence so Gabriel and Claire could arrive in utmost privacy. Only Dale and Lucille the chambermaid are allowed to serve them. They use the service elevator for the back-of-house staff—people who now are actually just serving a single person—which also opens directly on the penthouse floor.
