Muirhead, born in Perth, skippered Team GB's women to bronze in the recent Sochi Winter Olympics with a 6-5 victory over Switzerland.
The rest of Britain's curling side was made up of Scots, with Muirhead and her team winning the world championship for Scotland in 2013, but the 23-year-old admitted being part of Great Britain in a sporting scenario is second to none.
"For our curling teams, nine times out of 10, we represent Scotland at the European and World Championships, and that's a great honour to have your country on your back," she said.
"When it comes to the Olympic Games and you get a chance to represent Team GB, it makes it extra special.
"You're one big team and we're all together and it's a great, great feeling to know when you step on that ice that you are part of Team Great Britain and not just part of Team Scotland.
"So, for us, it just makes it extra-special as well."
David Murdoch, Muirhead's compatriot and captain of the men's curling side who took silver in Russia, is happy to let the debate run it's course.
"Scotland will decide, and whatever happens, happens," he said.
"We've had the full support from the whole United Kingdom and we're very happy with that."
Britain's Chef de Mission in Sochi was Mike Hay, also a Scot, and although he admitted nothing had been discussed if his nation were to break away, he echoed Muirhead's comments about being part of Team GB.
"I'm aware of the argument that's going on and that's obvious with the referendum coming up this year," he said.
"We are a sports organisation. We'll let the politics take care of itself.
"I hope I'm speaking for all the athletes here, that all the home countries are very proud to represent Great Britain.
"We don't have a Plan B here at Team GB. If that happens, we'll deal with whatever the consequences are."
All three were talking at a press conference at Heathrow Airport to celebrate the team's return from Sochi as Britain celebrated their largest winter Olympics haul since the inaugural 1924 games.
Skeleton gold medallist Lizzy Yarnold was also in attendance, as was Jenny Jones - who took bronze in the snowboard slopestyle event.