To succeed I had to forgot everything I had read before... and start again with this:
https://azure.microsoft.com/en-us/documentation/articles/power-bi-embedded-iframe/
ON AZURE PORTAL
Create Power BI workspace collection, and get access key (Provisioning)
GET A PBIX
From Power BI Desktop or a sample file
WITH A CLI
(must use that one : https://github.com/Microsoft/PowerBI-Cli )
Create a Power BI workspace
Import .pbix file into the workspace
Get report id
IN MY RAILS APP
(using https://github.com/jwt/ruby-jwt )
Embed the report into the web page
I can't tell about the many bugs encountered, or the signup/login problems with Azure... it was really painful to get there.
Cheers everyone.