Uhh, SpaceX isn't out to launch satellites. They just sent their Dragon cargo "ship" to dock at the ISS to deliver some stuff, the first of about a dozen more planned missions. Pretty sure no one else has done that
Space X is also launching satellites. They have over 40 launches booked and not just with NASA. They have a whole list of customers if you look on there website.
What is different about Space X and how they are working with NASA compared to other companies. Usually with NASA they work closely with the company building the hardware and have their mitts in the design process and they then take delivery of the vehicle. Kind of like how the US military procurs hardware. They ask for very specific design requirements and then pay for development of the hardware, take delivery and then own and operate the hardware.
With Space X, basically NASA has said we need to get cargo and eventually people up and down to ISS. We have requirements in how you will dock and approach with the ISS however other than that you are free to design and build the hardware as you see fit. We are here to assist if you have questions and you need some technical ideas etc. Oh yes you will also be responsible for launching and operating the vehicles. We will take over when you get the vehicle close enough to the ISS that we can grab it with the robotic arm. So basically Space X was free to design and operate the vehicle and NASA is just a paying customer. You didn't have some congressman insisting that some piece of hardware be built in his district and have hundreds of inspectors getting in the way of the building and operations of these vehicles.