They probably did for all I know, but likely used Nixon as the origin of the quote without knowing. Or maybe they were just referencing the OG war movie.

this just keeps getting funnier the deeper I go, the movie that Nixon got it from is a 'war comedy' lmao:

The idea is that a bayonet stuck in the soil can detect a land mine without setting it off; the mines are designed to detonate under heavier pressure. The 1970 cult-classic war comedy Kelly’s Heroes features a scene in which Clint Eastwood, Don Rickles, and the rest of their platoon undertake just such a task after one of their buddies steps on a mine and is killed. (When Rickles’s character, Crapgame, encounters a buried explosive and is asked what kind it is, he retorts: “The kind that blow up! How the hell do I know what kind it is?”)

https://politicaldictionary.com/words/probe-with-bayonets/