This is a great question! The short and simple answer is that using either it or they to refer to a corporation is correct. However, meaning is encoded in language, and so using one term instead of the other implies very different meanings. Let's start by looking at the definitions for both of these words:
It is a pronoun used to describe inanimate—or nonliving—objects.
Ex: The NFL says it will donate over $1 million dollars to the American Cancer Society.
They is a plural pronoun and is used to describe people.
Ex: The NFL says they will donate over $1 million dollars to the American Cancer Society.
Both of these sentences are grammatically correct. The difference lies in the implied meaning—using they to refer to corporations adds a human quality. Do you feel that these corporations are human? If not, then use it, which implies that entities such as the NFL, NASCAR, Coca-Cola, or Proctor & Gamble are merely objects, and should not be personified. Remember that both terms are correct, and this is more of a matter of voice—how do you want your audience to perceive these entities, as faceless firms or caring corporations?
*A special note: Academically, scholars agree that they should only be used in the plural sense; however, they is used in informal English singularly as well.
I would definitely say to use it. It can be difficult to distinguish between which one to use, but for me personally I find using it to sound the most correct. It seems to be mostly a personal preference, because the organization itself is an "it" (because it does not refer to people) but because the organization is made up of people, and people run it and keep it alive, it seems like you could also use "they" (because it refers to people). Sometimes, for example, when referring to a specific team in the NFL, I would say "they" but when referring to the NFL itself, I would use "it".
Hope this helps!