To say "everything" Red Hat ships being open source isn't quite true. There's a lot of proprietary code floating around, especially in the supporting infrastructure. When a product is put together, the upstream sources are bundled together and released - often behind the paywall.

Paul Cormier has it right - "We're an enterprise software company with an open source development model". Not an open source company.

However, you're correct. Red Hat's value prop is in top notch support.