Why can US deny airspace to commercial flights?
Every country regulates its airspace. You will find the ones for the US airspace on the FAA website. 

https://www.faa.gov/air_traffic/publications/us_restrictions/airspace/

What went wrong is speculation, but most probably had to do with Advance Passenger Information System (APIS). When filing a flightplan the passenger list is transmitted and the request for overflight was obviously denied.