I think the word private in "privately saved" should be in quotes, clearly.
Remember kids - firefox was built off the netscape navigator kernel. A download for FF is a vote for the right side of antitrust history (and therefore future)
This has got nothing to do with browsers. The article is saying that if you use an online Google service to save Google search results, then when they are forced to take said search result down due to DMCA then it also is (obviously) gone from the saved collection. This could just as easily happen in Firefox if you use Google's saved pages service, which is a bit like Pinterest. Meanwhile Chrome, like Firefox, never touches your actual bookmarks