It doesn't allow anyone to say definitively that the children had been at Treblinka. It allows anyone to say that the director of an orphanage was told by the children under his care who had been in several different camps that Treblinka was the worse.
It didn't say "Many of our boys have been in four or five camps, and if you ask them, they heard Treblinka, in Poland, was the worst." It didn't say "Many of our boys have been in four or five camps, and if you ask them, they say Treblinka, in Poland, was rumored to be the worst." It didn't say "Many of our boys have been in four or five camps, and if you ask them, they say Treblinka, in Poland, was the worst. But they don't really know because none of them were actually there." It didn't say "Many of our boys have been in four or five camps, and if you ask them, they say Treblinka, in Poland, was the worst. But they say the Huns put powdered glass in the soup so what do they know?"
There are no such qualifiers in what the director said. He said: "Many of our boys have been in four or five camps, and if you ask them, they say Treblinka, in Poland, was the worst" which suggests that the director believes that the children have a familiarity with several different camps, including Treblinka. It's value is tempered, not by the statement but by the fact that it's a hearsay statement that was told to a reporter.
But the statement is also vague and inconclusive. There is nothing to suggest that the 'boys' were actually claiming to have been at Treblinka. If they had been quoted saying 'we saw x' then this would be conclusive proof that they were claiming to have been at Treblinka. Instead they are introduced as having been at four or five camps, leading up to a generalising remark - 'Treblinka was the worst'.
Your fuss-making over absent qualifiers ignores the fact that there are equally absent qualifiers in the other direction, such as 'that they had experienced themselves personally'.
The best I can manage to prove 'transit' is credible evidence that 700,000 plus Jews were sent there during the war. There wasn't a Shtetl the size of San Francisco at Treblinka at the end of the war. The hypothesis that all the Jews were gassed, buried, dug up, incinerated, and reburied is nullified by the lack of evidence of mass graves large enough to hold the city of San Francisco anywhere near Treblinka. The only possibility is that they went somewhere else.
This vaguely worded out of context quote is nothing more than a third hand reference to Treblinka being the worst camp some children had experienced.
Your logic is, as usual, extremely biased. If you are going to resort to inference to the best explanation, which is what you are pretending to do, then you must obey the rules of inference, which means, paying attention to what evidence exists and weighing up both sides properly.
An honest examination of the evidence would indicate that there is more than zero evidence for Treblinka being an extermination camp, in the shape of the many witnesses, some documents confirming certain witness claims, and the physical evidence of the condition of the site in 1945.
By contrast, there is no evidence that Treblinka served as a transit camp for all the deportees. There is only the evidence that two transports were selected with a few hundred deportees going to Majdanek in spring 43 with rest remaining at Treblinka II to be killed, and that two or three transports were selected locally for Treblinka I, who were then returned to be killed at Treblinka II once they were worn out and useless as workers. Versus several hundred transports overall.
Whether the evidence for extermination meets your exacting standards or not is irrelevant, since there is much, much more of it than there is to suggest that 100s of 1000s of Jews "transited" Treblinka.
You don't seem to have noticed that you are resorting to deductive logic versus inductive logic
The only possibility is that they went somewhere else.
and that deductive logic will always lose to inductive logic when one is discussing empirical matters.
Indeed, there is a name for the fallacy that you have just committed, the fallacy of possible proof.
Either
prove transit, or prove something else. Don't waltz up here and handwave possibilities around as anything other than desperate speculation.
