Take this for what it's worth (we all know the reliability of support agents), but I attempted to get some facts directly from a Samsung support agent about the Verizon release date.
I wish I had better news than this, but it seems as though they know just as little about the release date as Verizon. The agent I spoke with gave a canned response of:
"Samsung manufactures devices and sells them to carriers. Once that occurs it is out of Samsung's control as far as the actual release to the public. Samsung gives a suggested date of release that they would like the carrier to follow, but the carrier is not obligated to follow the suggestion. I'm sorry I do not have any more information about the Verizon release of the Galaxy S3. I suggest you contact Verizon customer service about your question."
Maybe it is me, but that sounds like Samsung has been getting a barrage of calls with questions from not only the US, but every other country that is releasing the SGS3. I looked at it as a generic response they were told to give. I even asked about the rumored 6/28 release and the 7/9-7/11 release dates and she said "I cannot confirm or deny those dates."
Sorry I don't have better news. It looks like we literally will not know the ship date until people receive emails from Verizon informing us our shipment is on it's way and post on the Droid sites for everyone to see. Booooo.
I have to say I kind of grinned when I saw that the other carriers have supply issues. It made me feel a little less mad about having to wait. Either Verizon is a genius for planning on a shortage and waiting to fill initial preorders, or they are giant d-bags that don't care to inform anyone about anything ever.