No, not correct.

Although Chase points can be transferred to the frequent-flyer programs of JetBlue, Southwest, and United, they also can be transferred to some foreign frequent-flyer programs which partner with Alaska, American, and Delta. And in fact, you might even get a better deal on United flights by transferring your Chase points to a different program, such as Air Canada's Aeroplan, which is a United partner.

We can give much better advice if you are willing to provide your origination city, your destination city, and the approximate dates of travel. If you are able to depart from more than one airport to get a better deal, you should tell us that too. For example, I have friends who live near Princeton, NJ. While it's easiest for them to depart from Newark (a United hub), they can also depart from Philadelphia (an American hub) if significantly better fares or redemption rates are available out of PHL. You might not have that kind of flexibility, but we won't know until you tell us.