I am sure it is accurate. The iPhones that are sold as Verizon phones have their IMEI/MEID numbers in Verizon's system. If you buy a non-Verizon unlocked model, it will not work because the IMEI/MEID numbers are not in Verizon's database.
Some people have put a Verizon SIM in an unlocked/T-Mobile version and gotten SOME of the features to work, but it typically causes ongoing problems. If you're not in an LTE area, it won't fall back to CDMA for calls or data. Visual Voicemail doesn't work. I've seen other random issues reported.
A Verizon iPhone 5, 5s, 6, and 6 Plus will work on any LTE network because it is sold unlocked, per the FCC.