The 30-year-old Briton cruised through a second day in the Pyrenees mountains on Wednesday, finishing more than five minutes behind Stage 11 winner Rafal Majka of Poland but keeping his main rivals in check.
The bumpy, grueling ride under a hot sun came a day after Froome blew away the pack, prompting new suspicions about doping. Ironically, it came as Lance Armstrong — who was stripped of seven consecutive Tour titles — was to return to French roads nearby, even though he's persona non grata at the Tour de France.
Armstrong was to take part in charity rides Thursday and Friday to raise money to fight leukemia, taking the same route that Tour riders will cover a day later.
Froome brushed off Armstrong's visit as a "non-event", noting that "he's not on the start line with us."
However, Armstrong's presence is a reminder that any Tour leader can expect to come under at least some suspicion. To deal with that, Froome is willing to take testing even further.
"I'm open-minded to potentially doing some physiological testing at some point after the Tour, or at whatever point suits," the Briton said. "Obviously, there would be some interesting things that come out of it, and maybe as a team we might even learn something from it."
Speaking to French TV, Froome said he does "sympathize" with people who have their doubts about him, adding: "It's a normal question to ask" given the sport's history. But he emphasized his hard work — sometimes from 6 a.m. to 10 p.m. — and decried a "lack of respect" shown by some.
Arriving in France on Wednesday, Armstrong acknowledged to British broadcaster Sky News that he bore some responsibility for the spotlight now being trained on the Briton.
"I know what it's like for a guy like Chris to be in the middle of a Tour to deal with the constant questions, which of course he is. And to be fair and to be honest to him, a lot of that is my fault," Armstrong said.
However, Froome and his team are ready to take on the skeptics.
"Best moment of my day was stopping to have a chat to a guy calling me a doper on the way way back to the bus," tweeted Sky's Richie Porte, a key mountain guide for Froome in the race, after Wednesday's stage. The Australian went on to use an expletive suggesting that he had scared off the critic.
The day's glory meanwhile went to Majka, a 25-year-old Pole whose solo breakaway left behind a small group of rivals. The victory was the first for his strong Tinkoff Saxo Bank team and offered some redemption for the squad whose leader, two-time Tour winner Alberto Contador, has been struggling in this year's race.
Majka presented little threat to Froome. He had begun the 188-kilometre (117-mile) stage from Pau to Cauterets more than 44 1/2 minutes behind.
Majka, who last year won the polka dot jersey awarded to the race's best climber, burst out of a breakaway bunch on the way up the Tourmalet pass — the highest and most frequently visited Tour peak in the Pyrenees — and was the first over it.
The results had little impact on the overall standings. Froome leads Tejay van Garderen of the United States, who is second, by 2 minutes, 52 seconds while Nairo Quintana of Colombia is third, 3:09 back. Contador is sixth, 4:04 off the Briton's pace.
Defending Tour champion Vincenzo Nibali trailed more than six minutes behind Majka, again losing time to Froome.
Many seasoned race observers say it will take nearly a miracle for Froome's main rivals to topple him before the race ends on Paris' Champs-Elysees on July 26.
Appropriately enough, Stage 11 took the pack into the Roman Catholic shrine town of Lourdes, made famous because of a peasant girl's visions of the Virgin Mary over 150 years ago.
Livestock on the sun-baked, grassy mountainsides offered their own hazards for the speeding racers. France's Warren Barguil had to gingerly veer to the edge of the road on the fast downhill route from the Tourmalet as a pair of cows meandered across the road.
Thursday's finale in the Pyrenees offers more punishment, with a 195-kilometre (121-mile) trek from Lannemezan to the Plateau de Beille ski resort, featuring another uphill finish.