I can confirm this is not a true statement. Sorry Captain, as I love your advice in almost all cases....
I used a Verizon CDMA phones in Negril and Treasure Beach with a Digicel SIM both in September and December of 2015. Two in September and one in December.
Digicel maintains a CDMA system, as well as GSM, Flow (nee Lime) is GSM only AFAIK. Digicel supporting CDMA is the reason Verizon phones with Verizon SIMs can roam in Jamaica. If you do that though, you will be very sad when the bill comes.
This article clearly shows what Digicel does, and does not support in Jamaica. If you're a nerd like me, it will help: https://en.wikipedia.org/wiki/Digicel
Within the last few years, all Verizon phones have been SIM unlocked. It was a requirement the FCC imposed on Verizon as part of a deal that allowed Verizon to purchase a huge chunk of radio spectrum in the US. We used a Nokia Lumia Icon, and a recent Samsung Android with good results. We did try one AT&T phone, but could not use it as it was locked.
I had to reconfigure the internet APN to get data, but I'm guessing I would have to have done that for any network in Jamaica. I did not get LTE, but rather HSPA+ which is close enough.
I never did get MMS working, but there is also a separate APN for that, and I did not change it.
It is also true that the latest phones have radio chips that support CDMA/GSM/LTE. The iPhone 6 is a notable example. Keep in mind though, some of the carrier exclusive phones have firmware that cripples the phone for other carriers network frequencies.
Probably more than you wanted to know, but there you go. Put a Digicel Sim in that Straight Talk phone and you're good to go. Take it to the store when you go, and they will probably set it up completely for you (data and MMS) while you wait.
YMMV
Spiff