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".
Mixed bag of weather results in special weather statement for region
Areas north of the King-Snohomish County line, the East Puget Sound Lowlands, and the mountains are likely to see a lot more snow. Another round of winter weather is on the way for Greater Danbury and the Hudson Valley with snow and some mixed precipitation.
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.
Un convoyeur de fonds disparaît avec un gros magot — France
Un camion de transports de fonds a été retrouvé vide à Aubervilliers (Seine-Saint-Denis) ce lundi matin. La société Loomis contactée par Le Figaro n'avait pas encore réagi en début d'après-midi.