Wrong! The flag "Unicode" inside the connection manager (for the Flat File source) does mean any Unicode it ONLY means "UTF-16". However, this is not noted inside the help:
Indicate whether to use Unicode. If you use Unicode, you cannot specify a code page.
So, if you have to deal with UTF-8 file as I did, you need to deselect the "Unicode" check box and select as Code page "65001 (UTF-8)". Tricky.