Verizon phones are now locked if purchased on a payment plan. You may have just found some old verbiage on the website that they have not updated.
Basically, in 2008, the United States had a 700 Mhz radio spectrum auction that AT&T, Verizon and other companies participated in. Google also participated in the auction, but their motives were not to win, but rather drive the bidding up past the reserve price so that the spectrum will definitely sell and would prevent a spectrum auction with less rules on the spectrum. Google was basically acting if favor of Net Neutrality. They figured if they were "in the game" for buying it, they could suggest rules to the FCC about how the spectrum could be used. The rules were put in place and basically said that any networks or devices that used the frequencies had to be "open." Verizon NEEDED this spectrum to build their LTE network, so they were forced to accept (although they tried to sue, to get them dropped on constitutional grounds).
Basically, for Verizon to be able to build a network using band 13, that network must accept unlocked compatible devices. And for them to sell devices intended to be used on band 13, those devices had to be unlocked. And they did it.....
These rules were put into place by the FCC of 2008. Obama's FCC. Pro net neutrality FCC.
Fast forward to a few months ago. Verizon now locks it's phones... not because the rules were dropped, but because the current administration's FCC will not enforce the rules. The current FCC is headed by Ajit Pai... the same guy that killed Net Neutrality rules. The guy that used to work for Verizon. Ya that's him.
So yeah... Verizon phones are locked now.