I have good anecdotal evidence of this. Of the 9 PhD programs I applied to, I only visited 3. Of those 3, I was only accepted by 1.5 (one offered me unfunded MS admissions) and waitlisted by the third until I was ultimately rejected. The other 6 summarily rejected me.
The PhD program which took me on with full funding was the only one for which I actually contacted a professor I wanted to work with, and met with him. It was only students and admins I met at the other two schools. This program by the way was the strongest by most any metric of all the schools I applied to.
So, I'm seeing a definitely strong correlation between "Talked to Professors", "Visited the Department" and one's results. Quite surprising. Now I wish I hadn't spent so much money applying to so many schools...