FORTUNE — When University of Missouri defensive end and likely NFL draft pick Michael Sam announced publicly on Sunday that he is gay, reaction to the news that the NFL would have its very first openly homosexual player was mostly positive.

Other NFL players credited Sam for being brave and called him a pioneer. First Lady Michelle Obama tweeted that Sam was “an inspiration to all of us.”

But when Sports Illustrated surveyed eight NFL insiders — executives and coaches whose identities are anonymous — their responses to Sam’s announcement were strikingly different.

A personnel assistant at the NFL told SI that adding a gay player to a team would “chemically imbalance an NFL locker room and meeting room.” A league scout predicted that Sam’s stock as a draft pick would sink: “I just know with this going on this is going to drop him down. There’s no question about it. It’s human nature. Do you want to be the team to quote-unquote ‘break that barrier?’” Another person told SI that Sam’s sexuality would be a distraction for the team, which would count as a strike against Sam on draft day.

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Those statements stands in stark contrast to the NFL’s policy against discrimination based on sexual orientation that the league re-released in April 2013 after several draft prospects complained that they’d been asked if they had wives or girlfriends. The policy states that “there will be no discrimination in any form against any player by the Management Council, any Club or by the National Football League Players Association because of race, religion, national origin, sexual orientation.”

If the comments made to Sports Illustrated are any measure, the league’s policies can be considered abject failures. And in this sense, the NFL is just another workplace where policy and culture fail to meet.

It’s certainly not easy to get dozens, hundreds, or even thousands of employees to adhere to a common code of conduct, but a two-pronged approach is best, says GLAAD president Sarah Kate Ellis. One prong is instituting internal policies against discrimination, she says. But that’s not enough. A company must also exhibit those corporate values to the outside world. “Senior management and executives set the tone and culture at a corporation,” Ellis says, so their public recognition of LGBT rights carries a lot of weight.

Likewise, when the Human Rights Campaign compiles its Corporate Equity Index, which measures corporations’ LGBT policies, it ranks companies based on four criteria: explicit workplace protection based on sexual orientation and gender, fully inclusive benefits for LGBT employees, workplace resources that are dedicated to nondiscrimination policies, and public support for LGBT equity.

In releasing its statement on Sunday, the NFL missed an opportunity to address that last criterion and incite a larger cultural change. Instead of applauding Sam for coming out and reiterating its supposed inclusiveness, it reacted as if his announcement was an isolated incident: “We admire Michael Sam’s honesty and courage. Michael is a football player. Any player with ability and determination can succeed in the NFL. We look forward to welcoming and supporting Michael Sam in 2014,” the statement said.

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Efforts to stop discrimination at the private level are particularly important because firing an employee for being lesbian, gay, or bisexual is still legal in 29 states. Terminating the employment of a transsexual individual is legal in 33 states, Ellis says. That’s due in large part to the House of Representative’s failure to pass the Employment Anti-Discrimination Act, which would ban workplace discrimination against gay and transgender employees. The legislation made it through the Senate in November by a 64-32 margin; it’s now stalled in the House, which has yet to bring it to a vote.

But as the NFL has demonstrated, policy isn’t everything. Ellis put it this way, “It’s one thing to be able to get married; it’s another thing to display that wedding photo on your [office] desk.”