That's exactly what it is... In theory it should work, in practice someone might object because the visa was obtained under "false pretences".

If you still decide to travel, you should at least bring all documentation you have from your application and back that up with your cancelled business trip....

But the Swiss generally are not the most flexible. And that you applied for business purposes and now decide to travel for leisure and entering another country might raise some red flags. Especially the business apllication (where an invitation letter is compulsory) and the leisure use now would be a big red flag for me when asked to make a judgement. And even though it's perfectly fine to enter via another country it might still get you some additional attention, and questions.

And formally having a visa doesn't guarantee you entry, that's up to the immigration offer to decide. So you take your chances on how they judge your story. The Swiss e-mail strongly suggests that you apply again, you cannot say you haven't been warned.