In K-Pax the alien even impressed astrophysicists at the planetarium by drawing its planet's orbits.
The alien was always restricted to a mental institution.
Why didn't they create a media sensation about the K-Pax Alien?
There were many contradictions in Prot's character -- on one hand, he had an astonishing knowledge of astronomy (some of the things he'd discovered were absolutely new to some famous astronomers); on the other hand, he was hospitalized in a mental institute due to the fact that he had many mental issues. The staff obviously concluded that they were dealing with a mentally insane genius. He was maybe quite a unique and non-standard patient, but regardless - he was a patient in a mental hospital.
Some people took this pretty seriously, and investigated his story, but you must remember that the entire situation ended pretty quickly -- throughout the entire film, they had very little time.
Prot had a "deadline" -- if it was a countdown to a return to his home-planet or to a complete mental breakdown, either way it was a real deadline.