If I am right, fiddler use a root certificate to directly issue certificates to websites.

I earlier had a problem using Fiddler with an application. If I understood the problem correctly, the application was specifically checking if the server certificate was issue by an intermediate certificate (which was not the case here). So it was failing everytime with Fiddler.

I think it's also the proper way to do things. I don't know any public certificate provider who directly issue SSL certificates.