American journalists claimed that 31-year-old Cantlay had caused a rift in the US camp over not being paid, with some even saying he was not wearing a cap in protest.
Players often do not wear caps at the Ryder Cup due to a lack of sponsor's obligations.
Cantlay, who has amassed more than $42 million in his PGA Tour career, also did not don headwear during the United States' victory two years ago.
"It's not about that. It's just about Team USA and representing our country," he said after reeling off three straight birdies to snatch a dramatic point with Wyndham Clark against Rory McIlroy and Matthew Fitzpatrick.
"That's all I've got to say about that (not being paid).
"The hat doesn't fit. It didn't fit at Whistling Straits, and didn't fit this week. Everyone knows that."
Cantlay's teammate Sam Burns quipped: "I didn't know it was such a big deal not to wear a hat."
The world number five holed a 30-foot putt on the 18th green and the majority of the American team looked anything but divided as they celebrated wildly on the sidelines, angering McIlroy.
Cantlay's heroics dragged the USA within five points ahead of Sunday's singles, but they will still need the biggest comeback in Ryder Cup history to lift the trophy.
The issue of whether or not players should be paid at the matchplay showdown was briefly a hot topic ahead of the 1999 edition when Americans were reportedly unhappy about the lack of prize money.
The PGA of America came to a compromise and money was donated to players' chosen charities instead.
European star Jon Rahm said earlier this week that he would pay to play in the Ryder Cup and home skipper Luke Donald agrees that the tournament should remain "about pride".
"Absolutely not," he said when asked if players should be paid.
"It (the Ryder Cup) represents true sport. You saw it with some of the passion at the end there.
"It's a passionate event. It's about pride. It's about representing your country. It's about coming together as a team.
"It's the purest form of competition we have, and I think because of that, the fans love it. There's no extrinsic motivation involved. It's purely, purely sport.
"That's what makes it so special."
Europe will defend a 10.5-5.5 lead in Sunday's 12 singles matches as they attempt to regain the trophy and deny their opponents a first victory away from home since 1993.
