I know. "Breaking the silence" used to be a moderate organization which served as a watchdog against rare but severe misconducts. It enjoyed full cooperation from the IDF and worked internally and much more descretly. But then their leadership changed and they became extreme left. They started faking and blowing up stories, and lost their commitment to the truth. Many Israelis, even from the moderate left, see them as trators now.
IMO, all extremists are equally harmful. And I repeat my moto about this: The only safeguard against all extremism is doubt.
I know Hagai Matar, who wrote the Article that you cited quite well. He is a wonderful writer in both Hebrew and English and a very honest person who truly believes in what he says and does. However, he and myself have a very different view about the role of journalism. We once had a long discussion about that when we were writing in the same project. I think that his writing is not journalism but PR. He is honest enough not to try to hide the fact that his articles and field work are biased. He believes that is the way he should act, and again, I appreciate that very much. Still, IMO, once he uses the misnomer, "The occupied Palestinians territories", and states that the main problem is the occupation itself, his article is no longer about "Breaking the silence", but about himself.
Which brings me to the question of weather I can bring examples of false testimonies by "Breaking the silence". Well I doubt it if there was a case where they published a story that was completely made up, but that is not enough. When a person gives a testimony in court, he or she swear to tell the truth, the whole truth and nothing but the truth. There has been many cases when "Breaking the silence", and other similar organizations like "Be'tselem", brought a very partial and out of context story, solicited soldiers to talk to them (in one case they were interrogating soldiers about the IDF's countermeasures to the attempts of Hamas to dig tunnels into villages in the Israeli side of the border with Gaza. Now how is this related to their cause?), and looked away from other sides of the story. I would give you some links, but they are all to Hebrew content.
Now don't get me wrong. I am much worried about the rise of right wing extremism in Israel in general, and in the IDF in particular too. But as I said, when two extremities meet, they empower one another, and what happens in reality is that the conduct of "Breaking the silence" and similar organization, only works against their cause. Especially when they write and talk to people in foreign countries who often don't even know where Israel is on the map. Hagai Matar, says that "Breaking the silence" does not support the BDS, but he should know that they give them lot's of fuel. The reality of the Israeli-Palestinian conflict is complicated and very hard to understand, and no oversimplified and one sided view of it is doing any good.