Take the following as truth: The answer has nothing to do with their cause, however, but with the simple fact that dictionaries are not exercises in bi-unique substitutability; in other words, if one of the senses of run is `operate' (as in She runs an engine factory ), that does not make it valid to assume that one can substitute operate for run in We run in the marathon every year .  Although recognizing this as a shortcoming of dictionaries and assigning it arbitrarily to what, for lack of a better term, we might call the  genius  of the language, might seem trivial to the casual observer, it is a valid matter for concern in the realm of lexicology.
Then the following statement: "Although one can assume that one can substitute operate for run in "We run in the marathon every year", many people do not" is true, false, or inconclusive?
Answer: Inconclusive