According to ESPN.com's Todd Archer, Local 100 of the United Labor Unions said Tuesday that Jones' statement violated the National Labor Relations Act because it showed he is "attempting to threaten, coerce and intimidate all Dallas Cowboys players on the roster in order to prevent them from exercising concerted activity protected under the act by saying that he will fire any players involved in such concerted activity."
In an interview with 105.3 The Fan on Tuesday, Jones made his stance on the matter clear.
"If you do not honor and stand for the flag in the way that a lot of our fans feel that you should, if that's not the case, then you won't play," Jones said, according to the Dallas Morning News' Kate Hairopoulos. "That's nothing new as far as that being my wish or the way I want the Cowboys. As to whether or not I will basically institute or do what I said I would just say...I would ask anybody to look at my record relative to what I say I'm going to do, and go from there."
Jones' decision drew praise from President Donald Trump, who previously called for owners to cut "that son of a bitch" who protests social injustice during the anthem.
Local 100 disputed Jones has the right as an employer to take such drastic action.
"You can't discipline somebody for something that is a right they have under the law, whether that discipline be termination or benching or giving a slap on the wrist or writing up in their files they've been a bad boy," Local 100 chief organizer Wade Rathke said, per Archer.
Unlike the NBA, the NFL does not currently have a rule that requires players to stand for the anthem. Rather, the league's game operations manual suggests players "should" stand while "The Star-Spangled Banner" is played, according to the Kansas City Star's Pete Grathoff.
However, NFL Commissioner Roger Goodell sent a memo to team executives and presidents Tuesday that said moving forward, the league office would like to see players stand for the anthem.
"Like many of our fans, we believe that everyone should stand for the national anthem," Goodell wrote, according to ESPN's Adam Schefter. "It is an important moment in our game. We want to honor our flag and our country, and our fans expect that of us."
As far as specific Cowboys players are concerned, defensive linemen David Irving and Damontre Moore both raised their fists when the national anthem concluded prior to Sunday's game against the Green Bay Packers at AT&T Stadium.
Head coach Jason Garrett told reporters Monday neither Irving nor Moore would be disciplined for their actions, per Hairopoulos.
Meanwhile, Archer reported a field agent will be tasked with investigating Local 100's allegations. If those allegations are substantiated, the case could then be brought to trial.