[NB I'm not in the US so I have no idea how popular these beliefs are - I suspect they aren't that common and perhaps quite understandable given the impact Vietnam had on the US].
It just seems odd to me. Most people I know in the US would be familiar with the term "Fall of Saigon", which would strongly imply the first option "We Won" isn't correct.
Even the pop culture doesn't seem to put out a vibe that suggests the US won. Most of the popular movies about Vietnam tend to highlight the horrors of war in general and not some romantic notion of victory, patriotism, glory, etc. Almost all of them feature scenes with the US soldiers talking about how misguided and poorly run the war was.
At best, there may be some people that think "we could have won" had the war been waged in a different way, but I don't even hear that often. In fact, the quagmire of Vietnam was used repeatedly as an argument against the war in Iraq.
Can confirm: quite common in the midwest. Wouldn't be at all surprised if it's a more common view, in this region, than that we simply lost.
Typical complaint is that Congress wouldn't let them do enough bombing, and/or placed too many restrictions on it, in addition to choosing to withdraw rather than keep fighting.
https://newrepublic.com/article/64982/the-other-vietnam-synd...
[NB I'm not in the US so I have no idea how popular these beliefs are - I suspect they aren't that common and perhaps quite understandable given the impact Vietnam had on the US].