Personally I think it's a play on words: The title originally was Spanish case plumbs depth of trans-atlantic [sic] divide on Web privacy. Plumb here means to measure the depth of a body of water;
I don't think it means trigger, you had it correctly the first time: exploring, using the first example on the free dictionary; http://www.thefreedictionary.com/plumb
For those who are confused, I used THIS website: http://e.mydigitalfc.com/PUBLICATIONS/DCF/DCF/2011/08/11/ArticleHtmls/Fight-for-the-right-to-be-forgotten-11082011161005.shtml ; (where the screenshot is from) in order to answer the question, in the comments below the question someone put in the correct link (It was correct for me, I couldn't open the other websites), and THAT is the link to the article I based my answer on. As you can see, it DOES say 'plumbs depth'. I did not change the title.