In other words, "Vote for me -- I'm easily fooled!" (Not that I think the administration was lying, just that that's the logic of what McGovern is suggesting.)
As for the rest -- either Jackson or Humphrey would have been stronger candidates than McGovern -- in fact, of all the available candidates in 1972, McGovern was undoubtedly the worst choice, in terms of electability, and he went on to prove it in one of the most inept presidential campaigns in living memory.
That business about Wallace is eyewash. I don't believe he would have run as a third party candidate in 1972; he tried it in 1968, and it didn't work. But he was having significant success in the Democratic primaries, and might have had enough delegates to force the nominee to kiss his ring if he hadn't been shot. That would have been quite a spectacle.
And do you notice that the media never refers to Wallace as a Democrat, even though he stayed one for the rest of his life?