Not quite. It would be based on where the site in question ranked the applicants. It would not matter at all where you ranked the sites relative to others, as you need to account for the site's ranked order list.
For simplicity's sake, let's say you ranked a site 2nd and the site ranked you 1st. Even if everyone else ranked them as first-choice, if they rank you higher, and assuming you don't match at any sites you ranked, then you would match there.
This excerpt comes from the APAGS book (Williams-Nickelson et al., 2019) which I recommend, if you don't already have it:
"Why is it so important for you to rank programs in the order in which you truly prefer them? The Match algorithm has been specifically designed to allow you to think only about your own needs and preferences, providing an opportunity for you to make ranking decisions in as pressure-free an environment as possible. The computer has been programmed to respect your rankings, and you will be matched to the highest-ranked program on your list that ranks you and does not fill its positions with more-preferred applicants."