You can be a sole proprietor for basically nothing. There's also two forms of limited companies requiring 20K/100K of capital. The 100 is actually 50K because you only have to pay up half of it upfront.
I found quite often when the Swiss explain something, they explain it with a degree of confidence that is not merited by the actual facts. They cut a few corners here and there to make it easy to explain.
That presumably just means that you have to register as a sole proprietor. Some countries have special freelancer/self-employed tax categories (or whatever), others don't.
They told me, there is no such thing a service contract between an individual and a company. I must be either hired or I need to have my own company.
I am not inventing this, simply repeating what the companies said, and they really meant it.