Everyone with a stock, unrooted Verizon S3 has that notification. It's being discussed in this thread, including a way to remove it if you're rooted - Ongoing wifi notification !
Since there's already an existing thread about this, I'm going to close this one. Feel free to make any further observations or ask any more questions in the above thread!
Current lineup: Note 3, iPhone 5S, Note 10.1 2014
Previous smartphones: Note 2, Galaxy S3, One X, RAZR MAXX, Galaxy Nexus, Rezound, Note, iPhone 4S, Bionic, Stratosphere, Charge, Vitality, Incredible 2, Thunderbolt, Palm Pixi Plus, Droid 3, Fascinate, Incredible, Droid Pro, Droid 2 Global, Droid X, Droid, Treo Pro, Touch Pro 2, Touch Pro, Q9m, XV6800, XV6900
Previous tablets: iPad Mini, Transformer TF300, Evo View, Transformer Prime, Transformer TF101, Thrive, gTablet