Verizon's (and Sprints) network is 'special' in the sense that they use a little bit different tech than T-Mobile and ATT. So, you can buy unlocked phones and have them added, but you have to be careful about which networks that the unlocked phone will support. Verizon uses a CDMA network, and what im talking about can be summed up by this paragraph I grabbed online:
In the US, CDMA carriers use network-based white lists to verify their subscribers. That means you can only switch phones with your carrier's permission, and a carrier doesn't have to accept any particular phone onto its network. It could, but typically, US carriers choose not to.
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So, to answer your question, if Verizon says it doesn't support that phone, then no, you can't buy it and move it over. They do offer some other cheaper phones though, they won't show them at the store though, you have to look online on their website.