Thank you griffin. I did modify nginx's configuration so the web root for the challenge URL (http only) would be the directory I've mentioned.
Also, reading a bit made me learn about the verification cache that lasts 30 days. If an account key X has proven to be in control of domain Y, this will be remembered for 30 days.
Finally, I'm very sorry but it was by mistake that I included the domain name i...ch. Do you think you could edit it out of your message? It will be in the history, but my client won't see that haha. It's OK if you refuse, it's my fault after all.
Cheers, and thanks Osiris too! Great community. Not always easy to understand all the parameters, but with help it's perfect.