WTF... Maybe it's at the discretion of the store to make that call, or depending on how high customer volume is at each store. I can understand if they don't want lines rapping around their building of people wanting to pick up their phone. Anyone wanting to go in just to buy a phone charger for their blackberry wouldn't be able to do so, which reflects poorly on the company.
Anyways, I got this confirmation email which states that I could get my phone via mail by the 24th (this is their aim). At the latest it says the 28th (not the 5th of July, like the rep at AT&T said).
Thank you for ordering iPhone 4 from AT&T. Your device has been reserved. Today was the busiest sales day in our history. Because of the incredible volume of orders we received, there is a slight chance that some customers may receive their devices between June 25 and June 28. Rest assured, we are doing all we can to ship devices to customers for delivery on the 24th. You do not need to take any action at this point.