Here is my take, for what its worth.
There is nothing wrong with reciprocal links. The problem is with paid links, mostly, and with excessive cross-linking. More genereally, the problem is with trying to manipulate the Google rankings. Never post a paid-for link without the 'rel="nofollow"' attribute (Google has posted other approved methods for flagging paid links). And avoid situations where you and another site cross-link large numbers of posts, especially if those posts aren't clearly related to each other. It starts to look like you and the other site are colluding to manipulate rankings.
You do want to check the originating site to make sure it isn't a scrapper or a spam site and you don't want to link to those, but otherwise you should be fine approving them. I think that is a polite thing to do anyway. Pingbacks and trackbacks are pretty ugly so you may want to make an 'editorial note' out of them, if you have the time.