The targeting of Froome has reached a point that Bahrain-Merida manager Brent Copeland said he had told his riders not to follow him because it was too risky, having seen his star man Vincenzo Nibali crash out of the Tour after tangling with a fan on the Alpe d'Huez.
Britain's Geraint Thomas, fresh from winning two stages in the Alps, remained in the leader's yellow jersey.
"We support and accept the decision by the race organisers to exclude Gianni Moscon from the Tour de France", Brailsford said. If I have to pull towards the end then I will. "It was pretty stressful so I had no idea".
The incidents make teams anxious fans are getting out of hand on the most famous climbs of the Tour.
Race organizers have struggled to deal with angry fans protesting Froome's participation.
Meanwhile, race director Christian Prudhomme has "called for calm" after incidents involving fans during this year's race. The riders on the Tour, and champions of the Tour, must obviously be respected, as they are by the large majority of the public. But at a stroke, it all went up again.
The race expulsion adds to the 24-year-old Italian's troubled disciplinary record after he was suspended last year for racially abusing FDJ's Kevin Reza during the Tour de Romandie.
Wiggins believes that a similar situation will be avoided owing largely to the respect that Thomas has earnt through his loyal service to Froome in past editions.
"As a Frenchman, I'm ashamed", Sky sports director Nicolas Portal said.
Still, that didn't stop one spectator from placing an aggressive hand on Froome's back in a gesture that the rider did not appreciate.
"I had just moved from America to Europe, from the junior to the elite category, from mountain to road racing", Bernal recalled.
For a third straight day, Thomas heard some boos as he appeared on the podium to collect his yellow jersey in Valence. "I am sure the future holds good things in store for him". We're trying to stay in a mindset where we're not distracted by it. "That's a question for the people on the side of the road".
The stage resumed after a 15-minute delay. "Sagan was too strong", he said.
But while Team Sky could celebrate, Team Dimension Data did not get the Mandela Day gift they were hoping for as Mark Cavendish was eliminated from the Tour for missing the time cut. "It's not an easy stage", said Froome. "We get on - for now, anyway". "A welcome easier day for the whole peloton".
"After a stalemate in the battle for yellow, Welshman Thomas retained his 1'39" lead over Froome, with Dutchman Tom Dumoulin (Team Sunweb) also emerging unscathed to retain his third place, a further 11 seconds back.