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They have two funny areas in this wording, one says you can't be "published on web pages" with competing ads but read on and it sounds like they dont want anything looking like google site wide, at least not if it's targeted ads. Then they go on to say "We do allow affiliate or limited-text links." of which ad brite is "limited-text links" and not targeted at all.
So I would thinks it's OK, but the easiest way to know for sure is to just ask them. They seem to reply eventually, just make sure you're very clear that the page in question has no Adsense on it, but other pages in the site do.
Get a ruling and report back to us :)
Competitive Ads and Services
We do not permit Google ads or search boxes accessing Google search services to be published on web pages that also contain what could be considered competing ads or services. This would include ads that mimic Google ads or otherwise appear to be associated with Google on your site. If you have elected to receive content-based Google ads, this would also include all other content-targeted ads. If you have elected to receive Google search services, this would include other search services on the same site and non-Google query-targeted ads. We do allow affiliate or limited-text links.
To me "web pages" does not cover sitewide and should be logically ok.