Why Spock used the Vulcan proverb about Nixon in Star Trek VI

This is a reply in a comment thread to a YouTube video.

I've meant to offer a reverse interpretation re Nixon for two or so years since this comment (or another one like it), but only now got myself to write it.

Spock's Vulcan reference to Nixon suggests, that after the devastating accident on the Klingon moon Praxis, Klingon Chancellor Gorkon as a politician was suddenly on precarious ground. Nixon might have felt his re-election efforts to be like that, when he sought a second term in office.

(Nixon's China visit was throughout 21–28 Frebruary 1972, the break-in at the Watergate hotel was on June 17 of that year, and plans to wiretap the Watergate complex were drawn up in January by Nixon re-election officials.)

Spock then suggests, that if the peace overture is not accepted by the Federation, the Klingons might seek to acquire Federation technology through force.

As it was, Chancellor Gorkon would have none of it, and that would further set the stage for his toppling. — Think a Bat'leth fight by a challenger to the throne.

Aware of this, Gorkon then went to the Federation in a last-ditch effort to prop up his position and maybe save his life, in the hopes, that there would not be any co-conspirators onboard the Enterprise, and then later on Earth.