The morning after the White House issued a statement claiming that President Trump is “supportive of LGBTQ rights,” the mood among LGBT advocates was wary rather than celebratory.

Late last night, after a day full of panic and speculation about a potential anti-LGBT executive order, The New York Times reported that the Trump administration would leave in place a 2014 executive order signed by Barack Obama that prohibited discrimination against LGBT federal employees.

“President Trump continues to be respectful and supportive of LGBTQ rights, just as he was throughout the election,” the White House said in a statement. “The President is proud to have been the first ever GOP nominee to mention the LGBTQ community in his nomination acceptance speech, pledging then to protect the community from violence and oppression.”

Crisis averted? LGBT leaders like Rachel Tiven, the CEO of LGBT legal advocacy organization Lambda Legal, don't think so. They say they’re not fooled by the White House’s statement claiming that Trump has been and will continue to be “supportive of LGBTQ rights.”

“What we are expecting continues to be an attack on LGBT people,” Tiven told The Daily Beast this morning. “Keeping a provision that makes life more fair for more Americans shouldn’t be news.”

Yesterday, Tiven was preparing for the worst. Like the leaders of many LGBT groups, she had spent the day hearing rumors that the Trump administration had an anti-LGBT executive order in the works for this week.

Throughout the day, Washington Post columnist Josh Rogin had been tweeting out new details from unnamed sources, painting a picture of a potential executive action that could roll back Obama’s 2014 protections for LGBT federal contractors, interfere with same-sex adoption, and even allow some forms of federal anti-LGBT discrimination on the basis of religious belief. It could be The Big One, LGBT groups feared.

“Given all the smoke, there must be fire here somewhere,” Rachel Tiven, the CEO of LGBT legal advocacy organization Lambda Legal, told The Daily Beast early last night.

Then, the landscape started shifting. White House Deputy Press Secretary Stephanie Grisham told NBC News contributor Mary Emily O’Hara in the late afternoon that such an executive order “isn’t the plan at this time.”

Then the New York Times report came out. The Washington Post is maintaining that a draft of an anti-LGBT executive order was “circulating in Washington over the weekend” but that draft—if it exists—has not surfaced and Lambda Legal has not seen it.

LGBT groups were not exactly thrilled with the mere preservation of Obama’s 2014 workplace protections. They drew attention to a handful of common themes: President Trump’s promise to sign the sweeping First Amendment Defense Act; the anti-LGBT records of Vice President Mike Pence and cabinet nominees like Jeff Sessions; and especially the impact of Trump’s current travel ban, which applies to immigrants and refugees from seven majority-Muslim countries, LGBT and non-LGBT alike.

Human Rights Campaign president Chad Griffin said in a statement that preserving Obama’s 2014 executive order was “a rather low bar,” placing focus instead on the “LGBTQ refugees, immigrants, Muslims, and women [who] are scared today.”

Ditto the National Center for Transgender Equality, whose president Mara Keisling said in a statement that Trump “is certainly not an ally to transgender refugees, transgender Muslims, or transgender people who depend on the Affordable Care Act or Planned Parenthood.”

ACLU LGBT project director James Esseks also drew attention to the LGBT immigrants and refugees affected by President Trump’s travel ban.

And in reference to Trump’s supposed support for LGBT rights, Esseks repeated the axiom: “Actions speak louder than words”

Trump’s July 2016 nomination acceptance speech, which the White House cited as an example of Trump being “supportive of LGBTQ rights,” firmly situated that support in the context of terrorism.

“Only weeks ago in Orlando, Florida, 49 wonderful Americans were savagely murdered by an Islamic terrorist,” Trump said, pledging to “do everything in my power to protect our LGBTQ citizens from the violence and oppression of a hateful foreign ideology.”

After applause broke out, he broke off from the teleprompter: “And I have to say, as a Republican, it is so nice to hear you cheering for what I just said.”

And when then-candidate Trump held up a rainbow flag on stage (upside down) at a campaign event last November—a moment that Trump supporters frequently cite as proof of his support for LGBT people—spokesman Jason Miller told the Washington Times that “[Trump] will protect all Americans from the radical Islamic extremists who perpetuate hate and violence around the world, unlike Hillary Clinton who dangerously plans for open borders.”

That association between Trump’s expressions of support for LGBT people and his focus on “radical Islamic extremists” has not been lost on advocates in the wake of this latest White House statement.

Tiven characterized it to The Daily Beast as “concern trolling for LGBT people” and an example of “the right-wing support for LGBT equality as fundamentally in opposition to Islam” that is “straight out of an international anti-Islamic playbook.”

“Suddenly, the administration is very worried about LGBT people when they want to use it to keep out Muslims,” she said. “We’re not falling for that.”

And even if President Trump’s rumored reversal of Obama’s 2014 executive order never materializes, LGBT advocates are still on high alert. There is a National Prayer Breakfast scheduled for Thursday morning that Tiven and others have cited as a possible platform for Trump to sign a “religious freedom” order that would carve out room for anti-LGBT discrimination—although such talk remains, for now, mere speculation.

In the meantime, LGBT attention is shifting from Obama’s 2014 workplace protections to other matters—like Supreme Court justices and cabinet picks—that could have a material impact on LGBT lives. And now, Tiven says, if Trump really does support LGBT rights, he has the chance to prove it.

“If he likes LGBT people so much,” she asked, “why is he choosing Jeff Sessions [as his Attorney General pick]?”