Hi Sébastien - one thing to check is the response from the server providing the csv. The headers that are returned when the request is made from the map viewer may be causing the CSV to be interpreted as something other than text (which would potentially cause parsing to fail, etc).
You can check this out using a browser's developer tools (Chrome has a great set). Esri technical support can assist as well. In the response headers from the request for the CSV, you should see content-type as a property. This is an example from the USGS for their recent earthquakes feed: