Apparently because, in some country in which Sun did business, someone else had already trademarked “OpenOffice”, but Sun’s lawyers believed the addition of “.org” was enough to sidestep that trademark.

I think in many jurisdictions, if someone else already has legal claim to a trademark, sticking “.org” on the end may not be sufficient to escape infringement. But, maybe under the laws of whichever country this trademark existed in, it was. Or at least, so Sun’s lawyers believed-hence, they were quite insistent on including the “.org”