They may have known, and Harold Wilson may well have known,
I can't recommend the Ken Burns "Vietnam" documentary series highly enough. It's crystal clear than Kennedy knew the US could not win. However they were also cornered into having to back up their own "communism is worse than devil worshipping" rhetoric. Which is a parallel to where Putin finds himself now.
Successive US administrations knew that not only could they not win (so they were simply sending conscripts to die). They couldn't even hold on.
I'd have no problem if Nixon was called a war criminal. Bearing in mind we now know he was certainly a traitor.