I don't follow. Would you say that tumblr has very little original content? That's basically similar to what this service is, only it also automatically tweets a link to your rich tweet for you.
Ok, now I get how it works. I would presume the site contains a lot of rich tweets that are very thin on content then, even if there are some that are rich in content. That's what Google has a problem with. If I were site owner, I'd put noindex on pages with less than X words, and not put Ads on those tweets as well.
In general, Adsense on a very generic site like this isn't that effective anyway. Ads aren't very targeted and Google also doesn't like that. They don't want advertisers to have a poor experience.
You are right. Adsense is also not effective on this site, but Adsense was the only way to monetize the site. Google deactivated Adsense without any warning, so I had no time to remove Adsense on pages with little content.