"may play role" is such a vague phrase, it makes the rest of the sentence meaningless.
In the past, if the media said "The President may have have committed perjury", they'd actually lay out the evidence - President testified X, but documents suggest X is untrue.
Today it seems like "may have" is just a cop out for generating smoke where there is no fire. And when someone comes back and says "you actually have no evidence that's true" they say "well, that why we said 'may have'".