Steven Greenhouse was a reporter at The New York Times for 31 years and was its labor and workplace correspondent for 19 years. He is writing a book about the past, present and future of labor unions and worker advocacy in America. He is author of " The Big Squeeze: Tough Times for the American Worker" (Knopf 2008). Follow him on Twitter @Greenhousenyt. The opinions expressed in this commentary are solely those of the author.

(CNN) The Sinclair Broadcast Group has come under heavy fire for giving its local TV anchors an unusual order -- they were required to read statements that appear to echo President Donald Trump's tirades against the news media. Just imagine the crisis of conscience that many of these news anchors must have felt -- being made to parrot words that many thought were blatantly false.

Like many journalists, these anchors have spent years, even decades, building reputations for truth and integrity. And then Sinclair, the largest owner of local TV stations in the nation, was requiring them to read scripted lines, including "some media outlets publish these same fake stories...without checking their facts first," and "... some members of the media use their platforms to push their own personal bias and agendas to control exactly what people think."

It's hard not to feel sorry for them. No doubt many of them felt trapped. If they refused their bosses' demands, they could get fired.

Sinclair's order was in many ways making working conditions intolerable for these anchors. In the United States, when employers make conditions unbearable or unpleasant, there has long been an option that workers can pursue: form a union and seek protections through a union contract.

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If Sinclair's anchors and other journalists unionize, they can demand a contract provision that gives them a right to refuse to read statements they reasonably believe to be false or propaganda. One can call this a conscience clause or a clause to protect one's reputation for truth and integrity.

Sinclair owns 173 local TV stations nationwide (most of Sinclair's stations are CNN affiliates -- meaning CNN shares content and resources with them and vice versa), and some of its anchors in large cities are already in a union, SAG-AFTRA. Some of their contracts contain language about journalistic integrity, but generally nothing that specifically protects them from what Sinclair has required them to do: read propaganda, SAG-AFTRA officials told me. That is a requirement TV anchors in the US have rarely faced before.

Sinclair's management would probably oppose such contract provisions, but Sinclair's anchors and journalists can make a strong case that they -- because of their reputations for integrity and because of their news organizations' supposed dedication to the truth -- shouldn't be required to read or say anything they reasonably believe to be false or political propaganda.

If Sinclair's management is intent on having these propaganda-like statements read on air, then let Sinclair executives read them, instead of forcing local TV anchors to do so, thereby eroding the anchors' most precious asset: their reputations for integrity and accuracy.

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Some people have said these anchors should have quit instead of docilely reading something they believe is inaccurate propaganda that slimes fellow journalists. But it's not so easy for them to quit. Under some Sinclair contract language that has been made public , its journalists, if they quit, could face substantial penalties amounting to 20% or more of their annual salary.

In recent years, digital media have seen a wave of unionization -- at Huffington Post, Slate, Salon, Vox, Vice, Mic, ThinkProgress. There's even a unionization drive at The Onion. In many of their contracts, digital workers have insisted on what might be called journalistic integrity clauses. Some clauses say journalists can't be required to write native, advertiser-backed articles, and some clauses require websites to have a sharp line of demarcation between native advertising and stories and videos prepared by their news staff.

Short of forming a union, Sinclair's TV anchors might have another way to refuse to read statements they believe to be false. Let's say 20 Sinclair anchors from 10 cities agree to refuse to read material they reasonably consider to be false. If two or three anchors get fired for refusing, they might have some legal protections, thanks to federal law.

Under the National Labor Relations Act, workers are protected from firing and other retaliation if they engage in concerted activities to improve their working conditions. Jointly refusing to read false statements would certainly be one way to better one's working conditions.

Sinclair would no doubt argue that it's reasonable -- and legal -- to fire any anchor who refuses an order to read a company statement, and would call that behavior insubordination not protected by federal law. The dispute over whether such firings are illegal might well go to the National Labor Relations Board or the courts.

That could result in a yearslong legal battle, and Sinclair might decide the wiser course is to avoid such a drawn-out fight (and unfavorable publicity) over firing popular, respected TV anchors who were merely trying to preserve their -- and their TV stations' -- integrity and reputations.