Wikipedia’s built-in search engine supports a bit of markup that excludes certain content such as navboxes and content quality warnings from the search index. However, Nominatim relies on Wikipedia’s database dump of backlinks, which doesn’t have that kind of granularity.
I removed one of the navboxes, which doesn’t belong there, since it doesn’t even provide navigation to the article. On the other hand, this means it doesn’t contribute to any other articles linking back to the article. It only serves to boost the page rank of colleges and universities in the region.
Apart from that, on the English Wikipedia, it isn’t unusual for a county article to contain a navbox about the county that links to all the county subdivisions and another navbox about the state that links to all the counties (among other things). This means all the county subdivisions and all the other counties will link back to the article.
The article for the City of Cortland should have quite a few backlinks too via the county navbox plus another navbox of all the state’s county seats. However, it also includes the state navbox even though this navbox doesn’t link to individual cities and towns. If every place in the state similarly includes this navbox unnecessarily, then that could help explain the high number of backlinks.
In general, it isn’t surprising that a county ranks higher than even its county seat. Among the cases where a U.S. county contains a place by the same name, some of the places are more famous, while some of the counties are more famous. But unless the place is a tiny unincorporated hamlet, the user is more likely to want the place unless they qualify the query with “County”.