That being said, I think there are a number of reasons this time it might be true, which have been articulated by other folks in the forums.
First, Apple never broadcasts what it intends to do, but does on occasion, leak news to select outlets, like the Wall Street Journal. There have been rumors since the iPhone's inception, but those have come from mostly fan sites, blogs and Wall Street analysts (who know less than the fans or the blogs). The WSJ is the first credible mainstream media outlet to announce the news and it would not have run the story without some solid sourcing.
Second, it makes sense from a business standpoint to prevent Android from establishing a beachhead on Verizon, the nation's second-largest carrier. Since Apple's push is into mobile computing, they need to eliminate or mitigate any potential threats to the iPhone OS.
Third, LTE will take a few years to be established and I don't think Apple wants to give Android another two or three years to become dominant with Verizon's customer base. There will eventually be a single model iPhone that works on both AT&T and Verizon, but that's just not possible yet. It's not a huge technical challenge to build a CDMA iPhone or next yea, a CDMA-LTE iPhone. And I think U.S. customers are used to the idea that a phone on AT&T simply doesn't work on Verizon and vice versa.
Fourth, nothing has been mentioned on what Verizon might be getting or when they might be getting it. AT&T will certainly get the next generation iPhone, but that doesn't mean that Verizon will get the same thing at the same time. AT&T's contract with Apple might for example include a clause that says Apple can make the phone available to other provides, but AT&T gets exclusive rights to it for 90 days prior and pay the existing subsidy. And maybe Verizon gets an iPhone, but maybe it's the 3GS and not the fourth generation one, or it's the fourth generation one, but without as much storage.
Maybe I'm seeing the glass as half full or my outlook is rosier than most. I would certainly love to see a Verizon iPhone this fall, but if nothing's announced by September, I'm jumping ship to AT&T for the new iPhone.