I believe them when they say they don't share, but are you sure about that? Even advertisers that already have my full name and some data, they wouldn't want to link with what Google and Facebook have?
To be concrete, my local supermarket and Amazon have my full name, and partial purchase information (the supermarket via a loyalty card). Both have ways to contact me with promotions. You don't think they'd like to know what I like on Facebook (if I did that) or what I search on Google that might suggest purchase intent?
I think they'd love that data, the platforms just make more money by only allowing them to target with it.