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: Galaxy Note 2, Galaxy Note 8.0, MotoActv
Previous smartphones: Galaxy S3, One X, Droid RAZR MAXX, Galaxy Nexus, Rezound, Galaxy Note, iPhone 4S, Droid Bionic, Stratosphere, Droid Charge, Vitality, Droid Incredible 2, Thunderbolt, Palm Pixi Plus, Droid 3, Fascinate, Droid Incredible, Droid Pro, Droid 2 Global, Droid X, Droid, Treo Pro, Touch Pro 2, Touch Pro, Q9m, XV6800, XV6900
Previous tablets: Transformer TF300, Evo View, Transformer Prime, Transformer TF101, Thrive, gTablet