Robert_Charlton - 8:15 pm on Aug 21, 2013 (gmt 0)
I have checked a few of the sites that have asked me to remove the link to them and arguably they do look a bit keyword stuffed and over-seo'd so perhaps that fact COMBINED with my link is tripping the filter.
That's an interesting point. It's a good idea, if you have what amounts to a mini-directory on your site (and effectively it sounds like you do), to routinely check where your outbounds are going anyway.
...and also allow the business in question to submit a manually-reviewed link to themselves.... I code for each link and link the business with anchor text "Business name widget seller".
The anchor text, I'm sure, is one of the things that jumps out at Google. It could look like a bought link, intended to influence organic rankings.
Also... with regard to the listings the business submit to you, "manually reviewed" is not the same as edited. It may be that you need to edit your listings more. This might be a helpful wakeup call. I'd take pains to make sure that you are not simply using boiler-plate content that businesses submit. Possibly, Google is viewing these as cookie cutter listings intended to get self-placed backlinks. Look at the sites, evaluate them, and curate and edit your listings. Uniqueness is a sign of manual review.
Acceptable directory style generally means that you use plain-vanilla business names or canonical urls as your anchor text. You can always have a non-linked short additional "Business type:" description identifying the business as a widget seller.
All this isn't any different from the way Google has looked at directory links for years. What's crazy about it is that many people who don't know what they are doing suddenly reacting to the alerts. That said, it's probably better to have the alerts than not.
So you might want to get rid of listings that are to sites of low quality and keep only the good ones, and to do enough editing and curation that Google does not consider the links to be self-placed. There might be a grey area where you'd want to nofollow some links and keep those listings, but I'm not a fan of nofollowing links I myself place and then send visitors to.