"After these changes are made and Google has crawled the site again, the content should naturally drop out of the Google index."
I've already shown that Google DID NOT crawl the site again.
I've already shown that Google DID NOT crawl the site again.
You apparently didn't read the next paragraph from the link I posted. There are basically two ways for the contents to disappear from Google's cache: (1) Natural disappearance the next time Google's spider crawls the site, or (2) Expedited removal by the web site owner using Google's removal tool.
It's hardly surprising that Moveon.org would pro-actively use Google's removal tool (which is available to anyone who wants their own web page un-cached) to delete the Betray Us page from Google's cache. The fact that Moveon.org didn't do so sooner, and hence the ad remained in the cache for a while, is just evidence of Moveon.org's lack of Internet competence and/or efficiency. But it is not evidence that Google did anything unusual to assist Moveon.org in emptying the cache.