Can colleges see other schools applied to through the CSS?

I looked on the FAQ for the profile and found this:

Q: Will the colleges be able to see the other institutions I applied to?

A: No, your colleges will not be able to see the other institutions you applied to.

However, most people on the internet seem to suggest otherwise. What is the current policy regarding colleges seeing other schools applied to?

Who is “most people on the internet”? And why would you believe them?

Various CC threads say that the profile shows all colleges the list of schools. Not sure why I would believe them, however.

Really? Please provide a link to some of these threads.

http://talk.collegeconfidential.com/financial-aid-scholarships/449583-css-profile-can-colleges-see-who-i-send-this-to.html

if anyone can find a recent, reputable source on this matter that would be appreciated

The thread you linked to is from eight years ago. Your recent, reputable source is the Profile FAQ that you have already found and that has provided an answer for you.