Sorry I'm late to the party oceanmedianow, but I see from your post in May that you were still trying to take on this PBN?
I looked at a couple of the sites in the network. I don't think the "paid advertising" links are a problem. Sponsoring local organizations is a valid way to get relevant links.
Also, the 2 sites I looked at have directory listings, where the client is listed. While the top listing is properly identified as "sponsored", they also have a "regular" listing with a link to their site. I'm guessing that all the other sites in this network are similar, so they end up with enough "natural" links in addition to the paid advertising.
Finally, the sites I looked at have a good amount of useful content, from what I can tell. Very localized info. I don't know how up to date it is, and the websites seem to be running super slow when I checked, so I'm guessing this is a fairly old setup. But those sites still seem to have decent juice.
A good test of this network would be to see if their directory listings ONLY included their paid clients, in which case it would definitely be shady. I didn't look into it that far.
I'm not saying Google would or would not approve of what they're doing, but they have created, what appears to my quick look, a bunch of sites that have relevant, local content that could benefit visitors to those particular places. Other than the fact that all the "guides" are linked to one another, they don't look especially spammy.
Just my 2 cents worth.