It's both. Think of your cameras and lenses as a high performance car. The speed and cornering is limited by the one thing that becomes the bottleneck. If you have a fast car with great suspension and tires, you're all set. But if a nearly identical car has lesser quality shocks or weaker springs, that one will be slow. Likewise if you replace the tires with smaller, cheaper ones, performance suffers.
Camera focus is the same deal. the time line of cameras, and the "professional level" of the body has built in a certain level of focus performance. You can, for example, lesson the quick / accurate focus of one of the high--end pro bodies by putting a so-so old lens, say one of the old 35-80's and end up with slower focus, softer shots, etc on the "best" body.
While putting expensive glass on a cheaper Rebel WILL certainly result in better shots than the same body with cheaper glass, that can only go so far, as well.