We had such a congressional fact check organization. It was called the OTA (Office of Technology Assessment). Sadly it stood in the way of institutionalized lobbying (The K Street Project), so the Republicans eliminated it shortly after they came to power in congress in 1994.
It was on borrowed time anyway. The OTA was a threat to the fiefdom of literally every other agency. Their job was to butt in and ruin everyone's gravy trains of "not quite graft".
Imagine the OTA weighing in on the recent net neutrality shitshow. Wouldn't have made the FCC look to smart would it have? That same threat existed for every agency and congress and the executive. Literally everyone wanted them gone.
