Mr Trump was in El Paso, speaking to a crowd of around 7,000, to make a case for building a wall along the border with Mexico.
"The President could see the incident and checked with us that all was ok".
Footage from Skeans' camera, tweeted by O'Donoghue, suggested he and his equipment were knocked off balance for around 10 seconds, as he was filming Trump's speech.
United Kingdom and Switzerland strike post-Brexit continuity agreement
But the request was rebuffed by the European Union which has said it will "not reopen the withdrawal agreement". The political wrangling will do little to reassure British business though.
Gary O'Donoghue, BBC's Washington correspondent, who also was there, said that the man had jumped onto the media platform and tried to smash the BBC camera. The alleged assailant is shown shouting: "F- the media".
He yells "fuck the media" twice before being led away.
"I didn't know what was going on", Skeans told the BBC, describing the push as a "very hard shove".
"This is a constant feature of these rallies - a goading of the crowds against the media", he said.
Swalwell first introduced the Journalist Protection Act in February 2018, which he said aims to protect "journalists in every corner of our country if they are attacked physically while doing their job".
As Trump makes case for border wall, lawmakers reach deal
The former Texas lawmaker failed past year in his effort to unseat GOP Sen. "Walls do not make us safer", he said. During O'Rourke's speech, there were chants for him to run for president, which he has said he would consider.
Danahar said he sent the security review request to White House spokesperson Sarah Huckabee Sanders, though Monday night's rally was a campaign event, not an official White House event.
Trump has frequently attacked the news media for what he views as unfair coverage, decrying some outlets as peddlers of "fake news" and "enemy of the people". According to the magazine, the El Paso police department is was "still gathering" information regarding the incident.
Video footage captured by Skeans shows the camera frame focus on Trump before suddenly pointing down toward a crowd.
Members of the media oftentimes are faced with harsh rhetoric at Trump rallies, but it's rare that things escalate this far.
Manchester United legend Paul Scholes appointed Oldham manager
Manchester United legend Paul Scholes has taken his first step into senior football management with League Two outfit Oldham Athletic.