Lesley Stahl: We've seen that some of these visas for Turkish teachers to come here are for English - for them to teach English. How does that make any sense?
David Dunn: I'm not aware of that. I don't-- I can't, I can't comment on that. I don't know. I have not looked intimately into the visas they bring in.
Lesley Stahl: We have English teachers in this country.
David Dunn: English teachers are typically not part of the critical -- or the deficit.
Mary Addi: Our tax dollars are paying for them to come over here and take our jobs.
Mary Addi was fired as a teacher from a school in Cleveland, Ohio -- part of a Gulen-inspired chain of 27 charter schools in the Midwest.
Mary Addi: They want to give you the impression that they're just hard-workin' guys over here to try to educate our kids because American teachers are just too stupid.
Lesley Stahl: As far as you know, why is an Islamic imam, which Gulen is, interested in setting up schools in the United States?
Mary Addi: Because it's a great money-making operation.
Gulen's followers can make money thru contracts to build and maintain the schools, but Addi has gone to law enforcement with charges that the schools also make money by bringing in foreign teachers in order to take a cut of their salaries. She says she learned this after marrying a Turkish teacher.
Mary Addi: And that's when he told me that every pay period, he would have to cash his check and give-- he had to give 40 percent of his check back because--
Lesley Stahl: Forty percent of his salary--
Mary Addi: --40 percent in cash. Yes.
Lesley Stahl: And you've turned documents over to various federal agencies that you say proves this on paper?
Mary Addi: Yes.
The schools dismiss Addi's claims, calling her a disgruntled employee. But federal authorities told us they take her seriously and are looking into allegations of immigration fraud and misuse of taxpayer money in various states, and whether it's somehow being funneled to the Gulen movement.
Then - there's the Internet, where there are incendiary blogs accusing the schools of secretly promoting "an Islamic agenda."
Lesley Stahl: You know there are various blogs that have accused these schools of being backdoor Madrassas.
David Dunn: Yes.
Lesley Stahl: So do you think there's a little bit Islamophobia involved?
David Dunn: I think there's clearly some anti-Islam bias involved in these blogs.
Actually, we looked into this and Islam is not taught at all. That would be illegal since these are public schools that go out of their way to distance themselves from any religious affiliation - even denying a connection to the Gulen movement.
David Dunn: I think what matters is the results in the classrooms. Are kids learning math, science, reading, writing at a superior level? And clearly in these schools that's happening.
It is happening: Newsweek voted two Harmony schools among America's top 10. More of these schools open every year across the country, and waiting lists just keep getting longer. Gulenists tell us the schools are about reading, writing, and arithmetic, not religion.
And Bekir Aksoy in the Poconos says the man behind the door has no hidden agenda: Fethullah Gulen hasn't even visited any of the schools.
Bekir Aksoy: He does not want to see the fruits of his work. He just speaks and encourages people to be good human beings.
Lesley Stahl: That's interesting because there are schools in Pennsylvania. I mean, not that far.
Bekir Aksoy: He has not seen any of them, believe me. He does not leave that room.