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.
You probably shouldn't have had them on pages with little content in the first place. You did break one of their policies, but if it's not effective anyways, you haven't really lost anything.