Actually, though he's simplifying it a bit, there is a good kernel of truth to that assertion.
The US and its SEATO allies struggled for years against the VC insurgency, including a huge buildup of troops between 1965 and 1968. While any large-scale engagement ended in a US victory, we were never able to do more than curtail the VC as they used -- quite intelligently -- classic guerilla tactics and we did not have enough troops to truly quash their insurgency (the accepted ratio required at the time was 10-1).
Then came the Tet offensive, where the VC attacked throughout Vietnam en masse -- and were decimated. They finally came out in the open and fought giving us the kind of fight we could really win, and which we did. So high was the casualty rate and so damaged was the VC infrastructure that Giap thought that NV might have to ask for terms. Until, that is, Walter Cronkite and the rest of the US media -- perceiving the US public's war weariness -- announced that Tet indicated that any hope of victory had been lost. At that moment they knew that we would not continue absorbing casualties in order to win.
After that it was all "peace with honor, etc." We accepted our defeat in the very moment of victory -- largely because a big slice of the US electorate was tired of the bleeding.
There were, of course, a number of other factors at play, but being "willing to have more dead" was a central facet of the whole thing.
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