I find this impossible to believe. Do you have any sources?
But in our case, one student actively turned down an offer from a top-3 private university in the US (ranking in our discipline) for a UK university. He specifically cited the funding landscape, since that university had had many of its grants canceled at the time, but of course did not rule out returning post PhD. He was a top student!
There are simply not as many positions available in the US.