If you have an audience, you have PR power.
In the lower-right corner of Google Maps there is a tiny link that says, "Edit in Google Map Maker". Click this link and you can edit Google Maps. Your edits get sent to Google and they'll approve/deny it in typically a few days.
the listing only shows up if you type the exact name of the hospital into the search bar, which is useless.
I don't mean the ranking but other aspects - like you guys blacklisted some domains which produce low quality content in wholesale. (I don't know if the algorithm was tweaked to detect and filter such sources or if it was a manual thing.)
Webmaster Tools has a crawl rate slider which operate on a site-by-site basis, and that's existed for quite a while now.
If you're asking if they can manually boost a site's ranking, hopefully that isn't what's being suggested.