And they're not necessarily slamming the powerful and outspoken Jones for suggesting his players will be benched if they disrespect the flag.
'He's the owner. Either you listen or you don't,'' Washington Redskins tight end Vernon Davis said Monday. 'And if you don't listen, then you won't play. It's all up to each and every individual.''
Jones was responding Sunday night to questions about Vice President Mike Pence's decision to leave an Indianapolis home game in protest of about a dozen San Francisco players who kneeled during the anthem. President Donald Trump tweeted after Pence's walkout that he had told his vice president to leave if any players kneeled.
Former 49ers quarterback Colin Kaepernick started the movement early last season when he sat on the bench, and later kneeled, during the anthem to protest racial inequality and police mistreatment of black males. He remains unsigned and wants to resume his career.
The 74-year-old Jones, also the team's general manager, said after a loss to Green Bay on Sunday that the NFL cannot leave the impression that it tolerates players disrespecting the flag and said any Cowboys doing so will not play.
They were the most provocative comments so far from Jones, a powerful behind-the-scenes force in the NFL and recent Pro Football Hall of Fame inductee who had already been clear in his support of standing for the anthem.
The NFL players' union had a swift rebuke Monday. Executive director DeMaurice Smith said Jones contradicted assurances last week from Commissioner Roger Goodell and New York Giants President John Mara that players could express themselves without reprisals.
'I look forward to the day when everyone in management can unite and truly embrace and articulate what the flag stands for, liberty and justice for all, instead of some of them just talking about standing,'' Smith said. 'We look forward to continuing our talks with them on this very issue.''
Many of the NFL's 32 teams have held meetings in various forms to discuss the issue since Trump said more than two weeks ago during a rally in Alabama that owners should fire players who kneel for the anthem.
In some cases, teams have struggled with their responses.
After Trump's criticism, the Pittsburgh Steelers agreed to stay off the field before the anthem. But Army veteran Alejandro Villanueva, an offensive lineman, stood at the edge of a tunnel with his teammates in darkness behind him during the anthem two weeks ago.
Villanueva said he was not making a political statement or defying his teammates, calling it a misunderstanding that was 'very embarrassing on my end.''
Miami coach Adam Gase recently created a team policy requiring players either to stand or wait in the tunnel. Three chose to stay off the field Sunday at home against Tennessee - Michael Thomas, Kenny Stills and Julius Thomas. All three have kneeled in the past.
Asked why he was responding to questions on the topic after previously declining to comment, Gase said, 'Because I thought it was time for us to address it.''
After several meetings over two days before a Monday night game in Arizona two weeks ago, the Cowboys and Jones kneeled arm-in-arm before the anthem. All of them stood during the anthem, with arms still locked. Otherwise, the Cowboys have stood on the sideline.
The Denver Broncos decided two weeks ago that they would stop kneeling after coach Vance Joseph met with his leadership group. The Broncos stood before their most recent game against Oakland, with receiver Brandon Marshall raising a fist. Denver was off Sunday.
'We just feel like as a team, it's bringing more negative attention ... than it is positive,'' safety Justin Simmons said. 'So, we made our point the one time we did it. The awareness of the social injustices are out there.''
During their bye last week, Atlanta players and coaches had a discussion mediated by a representative from the Ross Initiative in Sports for Equality. Falcons owner Arthur Blank invited the outside perspective, and the team has decided to stand during the anthem.
'There's no policy that was written or spoken about,'' Coach Dan Quinn said. 'It's more one that was really in the heart of brotherhood, that what we do, we'll do it together.''
Jones isn't the only owner who feels strongly about players standing for the anthem, but there have been no indications of teams requiring their players to stand. Mara has told Giants players he wants them to stand but supports their right to do otherwise.
'As a team we've had our talks about it and we're good to go,'' said Redskins running back Chris Thompson, among several Washington players to deny reports that they are required to stand. 'Our ownership, we've all talked about it. I think on our end, we're good.''