A Long Island woman named Michele Catalano posts photos of M-66 explosives (that look to me like extra-large firecrackers) publicly on Facebook. A few weeks later the local cops show up and ask her husband if they have any bomb-making equipment.

Instead of drawing the most likely conclusion, she instead blames this on local Long Island cops MONITORING HER GOOGLE SEARCHES. I am not making this up. And news organizations uncritically reproduce this claim:
http://www.theatlanticwire.com/national/2013/08/government-knocking-doors-because-google-searches/67864/

Public posts are public, and any number of people could have found it and tipped off the cops, or law enforcement could vacuum up all public photos and do some rudimentary image analysis to match against photos of explosives. We've known for years that police peruse Facebook, after all: http://news.cnet.com/8301-13578_3-20000550-38.html

The difference is that your Internet searches are supposed to be, well, private. And if somehow curious local cops know what you're privately searching for, that is a big story. Having curious local cops ask you questions about your public photos of explosives is not.