It comes from the fact that we also used to use the word crack for “railtrack embedded in the pavement” as used by trams (streetcars). To let the crack oxidize is to not do proper upkeep on that section of the track.
Though no one uses crack to refer to railway track anymore. So the translation is definitely the connotation that modern day dutch speakers would hear.
As an aside, in Dutch, this alliterates ("rust" is "roest" in dutch).
As an aside aside, the expression is passive in Dutch. A more direct translation would be "that can rust to me arse". The "to" there is also weird in Dutch ("aan").
As for English "rut", that word comes from Middle French "route", ultimately leading back to a Romanic origin which funnily enough also has a meaning related to "to break, tear" (https://en.wiktionary.org/wiki/Reconstruction:Proto-Indo-Eur...).
So, although the two are not directly related, their origins are surprisingly close to each other.
The saying is also used with comino (a cumin seed), pimiento (a pepper), rabano (a radish), all rather vegetarian, and culo (ass), and possibly other regional variants.
The "reet" in the Dutch expression of course also returns in "dat interesseert me geen ene reet".
At least in Amsterdam we use the expression like this.
And although I too only know the expression with the word "aan" in it, the translation by jauco at the start of this thread seems to suggest they also use it without that word.
What is actually the Flemish expression for this? "Den boom in" (=up the tree) is the closed one I could find.