I agree, that is very confusing. I couldn't find the rules on the Federal Office of Communication website. But I did look again at the rules on the Billag website in French here and in German here. There are too many negatives for my intermediate French to translate perfectly, and when I use Google Translator it appears to say one thing in the French version and the opposite in the German version. The translation from the German is "Only if no workable antenna infrastructure (satellite, antenna, cable, Internet) is available, there is no television set for the reporting requirement." but the translation from the French is "The reporting requirement does not disappear when no longer receiving system is in use (satellite, portable antenna, cable, Internet)."

EDIT: I received a better translation of the French, which now agrees with the German version: "The reporting requirement only disappears when there is no working reception system (satellite, portable antenna, cable, Internet)." Therefore, if you have a TV but have no antenna, no satellite dish, the cable feed has been officially plugged by the provider, and you do not pay for a special internet TV service (see above post) then there is no need to pay for the TV license.