search engine rankings and PR can be greatly influenced by them
True to some extend, if you have a backlink from a .edu page which holds original content, and because of most .edu sites thus pages hold information which is being linked to by many webmasters because of it's credibility as a means to provide information to their visitors such a page would gain a lot of authority in the eyes of Google.
And will therefor receive a good PR for that page.
But only for that reason, the amount of backlinks and the relevancy and as well as other authority sites that have links pointing to that particular page with the high PR value.
That is what brings .edu or .gov sites such authority and gaining a backlink from such a page is very helpful as you pointed out.
But as you mentioned it appears (the page or whole site perhaps?) as a link farm and therefor the backlink you may get from such a site isn't as special as another backlink from a newly launched blog with zero backlinks and PR.
The pages with .edu and .gov extensions are not by definition authority sites or have a high PR solely based on the extension.
Just like any other non .edu or .gov sites/pages they have to gain authority which is in most cases a natural result by providing original content or interesting content and their perceived credibility which is why the're being linked to by many webmasters and therefor gaining authority, and a backlink then would be of value.
Other then that it's a waste of time. And should you deliver a backlink to the pages you refer it could be risky for you, vice versa isn't a problem according to Google as this would be out of your hands (in most cases), you can't control who will be linking to you.
Extensions getting special treatment by Google is a SEO myth, it's the content that counts and the authority a page has created/received by having lots of backlinks from other relevant sites/pages.
