"t remains part of Great Britain"

The SNP have said that themselves. The Scots would still be British in the geogrpahic and cultural sense though of course we wouldn't be part of GB in the political sense in that GB is a constituent part of the UKofGB&NI. The unionist politicians and commentators scoffed at the SNP suggestions that we would still be British though it is as you say obviously true. In fact one Nat politician has even claimed that independence would strengthen the sense of Britishness. For some people it may be so. Some who support independence will swear blind that they aren't British. Of course what they are saying is they don't want to be British politically. If that were out of the equation they may well concede they are British in the other senses. Most Scots have no trouble being Scottish and British and European.