I always change my settings to be more private when I hear something "new and improved" has come out. ugh...
For the record though... those websites do not actually have access to your facebook account or info from it.
What happens is websites can put in FACEBOOK code on their sites. When you interact with that, as in clicking the "share" button that shows up there, you are essentially still interacting with facebook.
It's not really harmful to you or your computer, or your facebook profile. The only real concern is whether you want that info being out there, that you interacted with the site, etc... like, do you want friends that visit that site to see that you visited that site... that sort of thing.
The sites aren't doing any snooping, it's just facebook widgets working with the information you allow them to see.
Again, I personally have things as zipped up tight as possible simply because I'm a private(and possibly paranoid) person.

My biggest frustration is how everything facebook changes as far as security, you're often already opted in without even knowing the change happened. :/