The TweetPress creators' arguments about the API only apply to the background image and color scheme. The rest of the theme has not been addressed.

The rounded menu in the upper left isn't from an API call. Neither is the sidebar setup or that little word bubble tip under the logo. And the Twitter logo-knockoff certainly doesn't come from the API.

I think using the API in the manner it is used is quite a neat idea, but the rest of the design is the issue here, not the background image and color scheme. It's not so much inspiration as copying the entire thing.

Companies like Twitter, The New York Times, CNN, the BBC, Facebook, etc. pay plenty of money for their unique designs. I think it sucks that people make "clone" themes that pretty much mirror the look. Inspiration and "borrowing" are important parts of art, but direct copying isn't nice...