@Eyemgh- the national labs and other federally funded facilities you name serve a different purpose than the Federally Funded On-Campus Research Centers (FFOCRCs) such as the ones at Stevens and other universities. The national labs are government facilities that were paid for and built by federal agencies. The affiliated universities (such as Caltech which manages Jet Propulsion Laboratory, Princeton which manages the Plasma Physics Lab, et al) are contracted by the federal agencies that own the labs (JPL for example is a NASA lab, PPL is a Department of Energy lab, etc.) to manage their day-to-day operations. The affiliated universities did not develop or build those national labs, they are just contracted managers for them. So, suggesting that they are somehow unique or special in that they “have national labs”, is not really true. Those schools are hired by the government to manage them rather than the sponsoring agency running the day-to-day operations of the lab itself. Some of the employees of the national labs are employees of the university manager while others work directly for the sponsoring federal agency. Of course, the university manager also typically has students of their own doing work in the lab and conducting research projects. From the business standpoint this arrangement is no different for example, than an owner of rental properties hiring a management company to collect the rent, repair the plumbing and wiring, screen tenants, make sure the property taxes are paid, etc.
There are also private non-profit corporations that are designated as Federally Funded Research and Development Centers (FFRDCs). They are privately owned and managed, but they are chartered and funded by federal agencies to do research specific to those agencies (e.g., MITRE Corporation (Air Force and FAA), Battelle Memorial Institute (NIH, EPA, and others), Aerospace Corporation (which was the developer of GPS - Air Force), and several others.
BTW, I worked at one of the national labs so you need not tell me what their purpose, administration, or functions are.