Sure, but the story is not inherently about the EU. It's about the free movement between neighbouring countries, which is something Leave campaigners are determined to stop as part of our withdrawal. Leaving could've been over relatively quickly if all we did was leave the EU but keep our place in the single market.
Switzerland accepts freedom of movement of goods, services, capital, and labour between itself and the EU - freedoms which the Brexit campaign promised to remove and freedoms which make this story possible.
Switzerland is a Schengen member, this means no passport control at borders, but the UK is not, this means passport control when flying from the Schengen area to the UK.