This article does a very good job of piling on the evidence for the video being fake:
The evidence is primarily circumstantial, so far no one involved has explicitly admitted it was fake.
In the video there are four Gillette logos visible -- two behind home plate and two on a roof facade over the third-base bleachers. But those logos aren't part of McKechnie Field in real life, Trevor Gooby, the Pirates' director of Florida operations, told a reporter for Patch.com. The logos were added digitally and included in the final video that was posted on YouTube.
Already we know that some aspect of the video was altered. It would be a fallacy of generalization to then say that the catch itself was therefore also altered, but the evidence supports that theory.
The video itself was uploaded by a person who lists their company as Gillette and the recording itself was recorded following a 6 hour recording session for Gillette commercials featuring Evan, suggesting that it too is part of their marketing campaign.
If you're still looking for evidence that this was not meant to be part of an actual newscast,
there's the reporter and the video graphic identifying Longoria. There is no television station symbols or letters on the video, and the reporter is holding a microphone without a "flag" that identifies the station where the reporter works. Perhaps even stranger, we could not find the video posted on any news site. (Surely, a TV station would love to claim the video as theirs.)
The circumstances of the batting practice also seemed contrived, according to baseball reporter Topkin of the times.
Topkin noted several things that aren't typical during a batting practice session. There is no cage surrounding the batter to catch foul balls or stop pitches that aren't hit. There's also no screen protecting the batting practice pitcher. There are no coaches in the video hitting ground balls and no other fielders on the baseball diamond to track down any hits.
Furthermore, the batter himself acts oblivious to the entire event. He never yells a warning when the ball heads straight for the interview and crew, and after the catch is made, he resumes a normal batting stance and ignores the congregation in spite of the cheers from the other supposed players on the field.
On the physics side, while the initial hit and resulting trajectory is normal, a frame by frame of the video shows abnormal ball movement right when the catch is made.
The ball that's caught clearly comes from a different location and angle than the ball hit their direction. You probably saw this in the original video, but this was slowed down to 1FPS to make it more clear. The ball clearly doesn't move for multiple frames, then changes direction, [that's] clear video tampering.
Finally, the words of Gillette spokesperson Norton addressing questions about the video were a cryptic refusal to claim the video was real or admit it was fake, which is very much in the spirit of viral marketing campaigns:
The video was filmed while on location for a Gillette Fusion ProGlide commercial... We'll leave the 'is it real?' debate up to the viewers.
So as I said, primarily circumstantial evidence along with a fairly solid theory on the frames surrounding the catch being doctored, as the Gillette logos in the park were.