Unlocked is not the same and unbranded. If it was BUILT for one carrier, it's hard-coded down to that frequency. There are some people that say that with software that is illegal to own outside of RIM's factory/labs, you can get into the engineering code and change it. And, there are those that say it's the physical chip in the phone that does not have it.
Either way, if a phone was branded to one carrier, you can unlock it to work on other carriers, but not on all bands.
UNBRANDED phones have never been locked down to any carrier and should have all bands available.