Several years ago people would find a search that they ranked #1 in Google and then link to that Google serp. The logic being that the googlebot would follow the link and then realize that a mighty and powerful site like Google is linking to your site and thus pass huge link popularity to you. This “sorta” worked back then. It really does not work now. The reason is that the specific page needs inbound links to be able to pass outbound link popularity. Since you will probably be the only site linking in to that Google serp, it really doesn’t have any link power to pass along. Also you will form a reciprocal link exchange which is not as valuable as a one-way link pointing to you.
My suggestion is not to link to pages just because they link to you. You will have better results if you spend time searching the engines for sites listed under related keywords and asking if they will give you links. For example if your site sells widgets, look at sites that rank in the search engines for “history of widgets”. These sites will be related to your widgets site and probably not a commercial site if they are focusing on history. They will probably be more open to giving you a link.
While they may not have inbound links to them, does authority not have any benefit in itself?
And yeah, I know that a Google SERP will be discounted, but if there are ways to encourage authority sites to come up with a link to you programatically, I could imagine that the links might add *something*. Of course, I don’t do this for a living… yet.
Additionally, it’s only reciprocal if you link from the same website that’s on the page you’re linking to.