I'm thinking he might have conflated two points: you can see the demographic breakdowns of people who click various ads, and the list of people who 'like' your page is, of course, public.
They can see a list of people that like they page. They can only see the information you've made public on your Facebook profile just like anybody else who is on Facebook but not on your friends list.
I work with fb ads, there is no way to get any information from people who click on your ads apart from the fact they fit the demographics you set on the ad.
Whoa, what? Advertisers can see my Facebook profile if I click their link? Talk about oversharing...