I recall with Earl I think the NHC and Canadian Centre debated when Earl was no longer a hurricane. So disagreements can occur. However the WMO declared the NHC the primary center for tropical forecasts so to my knowledge staff members coordinate with foreign government to issue warnings. While its up to that local government to issue the warnings, I have yet to hear an area to go against NHC recommendations. Is that about right Patrick?
That's my understanding, too. The National Hurricane Center has sole
official responsibility for investigating and issuing reports and advisories on tropical cyclones in the Northern Atlantic and Northern East Pacific. However, that doesn't mean that other countries have their own tropical forecasting bureaus. Canada, actually, only relatively recently started its own tropical forecasting. Now that the National Hurricane Center has stopped issuing advisories on Igor, Environment Canada is the only meteorological organization (that I'm aware of) that is.
Even though it's the official forecaster and advisory issuing organization for tropical cyclones in these two oceans, the NHC only issues watches and warnings for the United States. Each country alone has the authority to issue weather advisories for its own territory and coastlines.