Can India overcome fake news when the ruling Bharatiya Janata Party is often complicit in peddling it? The question arises from the latest skirmishes between the Narendra Modi government and the media. On Monday the Ministry of Information and Broadcasting in Delhi announced guidelines that would allow it to suspend the official accreditation of print and broadcast journalists for creating or propagating “fake news in various mediums.” Faced with an outcry from journalists, the government withdrew the guidelines the next day.

The abortive clampdown comes amid a heightened media focus on politically well-connected fake-news sites. Last week police in the southern state of Karnataka arrested Mahesh Vikram Hegde, a co-founder of Postcard News. Mr. Hegde’s arrest was sparked by a tweet that showed a picture of a visibly bruised Jain monk with a caption claiming that the holy man was “attacked by Muslim youth.” The monk had in fact been involved in a minor traffic accident.

Those familiar with the site would not have been surprised. Postcard News once falsely—some would say laughably—suggested that prominent television journalist Barkha Dutt hitched a ride to an assignment on a Kashmiri terrorist’s motorcycle.

Postcard News also published a florid fictional account of a businessman who supposedly surrendered 60 billion rupees (about $900 million) to authorities in response to Mr. Modi’s 2016 decision to scrap overnight nearly 90% of India’s currency by value. The site also fabricated a story about Delhi’s most prominent mosque, the Jama Masjid, losing its electricity connection over unpaid bills, a canard that found its way to television news.

In many countries, someone like Mr. Hegde would be cordoned off from polite society while he duped unsuspecting rubes on the internet. In India, several BJP ministers have shared Postcard News stories on Twitter, and Mr. Hegde’s account is one of fewer than 2,000 Mr. Modi himself follows. After Mr. Hegde’s arrest, those on Twitter who demanded his release included BJP ministers and a slew of social-media influencers widely viewed as supportive of the party.

In many ways, Postcard News highlights the difficulty of cracking down on fake news in India. While no ideology or party has a monopoly on the phenomenon, a clutch of fake-news sites in both English and Hindi promote an agenda in sync with both hard-line Hindu nationalists and the BJP government.

That means any genuine effort to clamp down on fake news would likely end up hurting the BJP disproportionately. Companies such as Facebook —India’s more than 240 million users are its biggest market—will have to tread much more gently in India than in many other countries. In the West, the primary threat from fake news often comes from foreign governments—for instance, Russian bots allegedly trying to sway American or French voters. In India it comes from friends of the ruling party.

In a maneuver American readers will find familiar, BJP leaders have begun to describe any news that embarrasses the government as fake. Earlier this week at least 13 federal ministers took to Twitter to bust what they called “fake news” by sharing a story from a self-styled fact-checking website.

The only problem: Much of what the website, and by implication the ministers, deemed false was plainly true. This included a newspaper report on a government directive to officials to stay away from events marking the 60th anniversary of the Dalai Lama’s exile in India. (A government minister and senior BJP leader later attended a Tibetan function in Dharamsala in an apparent effort not to lose face over kowtowing to Beijing.)

Technology amplifies the problem. In the U.S., Facebook and Twitter play a primary role in spreading false news, says Soroush Vosoughi, a data scientist at the Massachusetts Institute of Technology who has studied the subject closely. In India the main culprit is WhatsApp, which reaches at least 200 million Indians and has become a primary source of news.

According to Jency Jacob, managing editor of the Mumbai-based fact-checking site BOOM, anonymity makes fake news on WhatsApp harder to trace and refute. Last summer, mobs in India lynched seven people after viral WhatsApp messages falsely reported that gangs were abducting children.

The problem is exacerbated in India by the mismatch between fact checkers and its burgeoning fake-news factories. The country’s three most prominent fake news busters—Alt News, BOOM and SM Hoax Slayer—count fewer than a dozen fact checkers among them, and these include unpaid freelancers who contribute out of a passion for the job.

According to Mr. Vosoughi, the MIT researcher, falsehoods continue to travel faster than the truth. “If a baby is born and I write a story saying it has two heads, it makes it more interesting,” he says. “More people will share it. If you’re writing false things, you have more leeway than if you’re writing the truth.”