One year ago, the filmmakers Tia Lessin and Carl Deal thought they had hit the public television jackpot. ITVS, an arm of public television that finances independent documentaries, had signaled interest in subsidizing and broadcasting a film about the influence of big-dollar donors on elections. At the time, Ms. Lessin and Mr. Deal were calling their documentary “Citizen Corp,” and they were expecting $150,000 from ITVS to help them finish producing it.

Then a few things happened. Last fall, the film was renamed “Citizen Koch,” a reference to Charles G. Koch and David H. Koch, the billionaire industrialists who are major supporters of conservative causes. Around the same time, ITVS (through its “Independent Lens” series) gave the premiere of a film called “Park Avenue: Money, Power & the American Dream,” which was critical of David Koch and other rich New Yorkers. That film caused heartburn at WNET, the powerhouse PBS station in New York, where Mr. Koch was a benefactor and board member. By April, a few months after “Citizen Koch” had its premiere at the Sundance Film Festival, the $150,000 expected from ITVS had evaporated.

Now the money is back, but from a new source. After ITVS told Ms. Lessin and Mr. Deal that it was not going to finance the film or consider it for “Independent Lens,” spurring accusations of self-censorship, the filmmakers set up a fund-raising drive on Kickstarter. Last week, that drive passed the $150,000 mark, more than twice the original goal, in effect replacing all the money that ITVS had rescinded. Kickstarter said the number of backers — 3,400 — put “Citizen Koch” in the top 1 percent of all the campaigns the Web site has hosted.

But the filmmakers still do not know how the documentary will be distributed, beyond the DVDs they have pledged to send their Kickstarter supporters. They have looked at streaming services like Netflix; there have been conversations about a theatrical release, too. But PBS stations (by virtue of their being beamed over the public airwaves) are among the preferred ways for documentaries to reach audiences, and the best route to the stations — through ITVS — appears blocked.