This is my take on it:
If you only have three cars, then "one of those three cars breaks down" (that is still one in three) so "one in three breaks down".
If you have thirty cars, and ten of them break down then "one in three break down" (if you add up all the "ones", you get "ten" which takes the plural.)
The problem many people have with "one in three cars breaks down" is that they don't like "breaks" following "cars". The gut feeling is that "cars" should be followed by the third person plural, not the third person singular.
The upshot is that I agree with Swan - both are acceptable.
Note that the correct spelling of his first name is "Michael". It is one of the most commonly misspelt names in English.
Student or Learner