I suspect it has more to do with money than safety. I would guess the safety issue is just a red herring.
I'm sure it has to do with BOTH. Uber drivers and vehicles should be subject to the same safety and inspection rules as any other vehicle for hire. Uber drivers picking up at the airport should be subject to the same rules and fees as other drivers.
Newspaper articles suggest Uber drivers are driving around the airport, looking at their Uber smartphones, waiting for a customer to pop up on their phone. Uber gives the fare to the driver closest to the requesting customer. That means drivers want to stay close to the terminal as much as possible.
Those Uber drivers are providing a service which is virtually identical to that provided by taxis. Instead of walking to the curb and signalling for a passing cab customers are doing the modern equivalent with a smartphone.
The fact that a customer is using an intermediary and an app to obtain transportation has nothing to do with applicable local laws and fees. Uber didn't launch service in NYC until they came to an agreement with regulators.