There has been much confusion around the triggering article 50 question which is unsurprising considering the lack of contingency planning . Some Brexiteers wanted it triggered asap as they don't trust the government to deliver Brexit and some remainers seem to think we are delaying because we are trying to avoid Brexit. It was always likely to be the best option to wait as it is in our national interest to do so.
As you point out the Swiss situation has some bearing on the free movement question. We also need time to establish our red lines,formulate a negotiating strategy and to gather the relevant negotiating expertise before embarking on years of complex political/trade negotiations. But most importantly we are in relatively strong position as the EU can't move forward until we officially start the exit process. We also still have use of our EU veto so could cause considerable problems if provoked.
It does look like the EU were bluffing re single market access = free movement which many of us thought would be the case despite continuously being told the opposite was a 'fact'.
I wouldn't say it was a "fact", just likely on the balance of probabilities. However, a lot is now up in the air, possibly as much to do with terrorism as anything else. One response would be to scrap Schengen....another would be to gradually erode the Free Movement of People principle. Perhaps both. With both French and German elections next year, who knows what might happen. One thing's for sure - the mainstream political parties in each country will have to fend off the far right, and may be tempted to do something which was unimaginable a few months ago. As a Remainer, I would love us to stay, but the next best option is continuing access to the Single Market with limits over free movement. You never know.