I am not completely familiar with Facebook's ad platform. Does it really let anyone see, for example, which demographics Procter & Gamble is targeting with a particular Gilette ad? (Or its Gilette brand, generally?)

For political ads you can also go to a page and look up all the ad campaigns they are running, how much money was spend, who was target, what the ad creative was, etc

Pardon me, I meant that anyone should be able to see who anyone else is targeting. Currently, when Terrible Kale Bar® shows me an ad, I can see it's because I liked a post of my Portland friend's. But I can't look at Terrible Kale Bar®'s page and see a list of whom they're targeting.