That's quiet easy. Children, especially in lower grades and in kindergarten often tell (exaggerated) tales to their peers and teachers. So teachers are very well informed about the most intimate aspects of a family's life, which may surprise even the parents. My friends with children had some rather amusing stories. The trick is to sift exaggerations from real threat signals.
The problem with the case of this Russian kid is that under the international law, what happened to him can be classified as an abduction of a foreign national. Plus this is an infliction of a gross psychological trauma on the child. In a normal world the child should have been transferred to the Russian child care authorities, which should decide what to do in accordance with the Russian law.
If I were ever separated from my parents in such a manner and learnt about it as an adult, I would have sued the bastards kidnapping me for million amounts for each day lost of my life with my parents. The reverse applies, and a lioness protecting her cubs would have seemed like a tame purring cat compared to my mother should something happen to her children. I remember as a 12-year-old I went for a month to pioneer camp. That was tough, being separated from the family, even though parents visited a couple of times. Here, a 5-year-old is a total isolation in a foreign country.
I can hazard a guess at what this 5-year-old has been through for the last 3 weeks of separation from the parents. He could feel anger and confusion at being, what he'd think, abandoned by his parents, who don't come to rescue him. Coupled with interrogations (sorry, "interviews") and possibly suggestive questions, the child may start wishing for the parents to feel the same hurt he is feeling and tell accusative stories, thus unwittingly sealing his own fate of being forever torn apart from the family. Alternatively the boy might start thinking that there's something wrong with him if his parents abandoned him, which will lead to insecurity, inferiority complex and potential future suicidal thought. In either case, this three-week separation has already done its damage.
The hearing deciding the fate of the abducted kid was today...