The Pope and all of the Bishops in full communion with the Pope and by extension all of the Priests under the authority of said Bishops told us to stop attending Mass for the time being. If the aforementioned entities do not constitute the authority of "The Church" then I don't know what does.
As for Msgr. Lefebvre and the issues relating to his excommunication then please be aware that this is a different issue altogether which I do not wish to delve into as it is unrelated to the above consideration.
Yes, they have the authority, that is not in dispute, it is because they have corrupted themselves and abused and misused this authority for 60 years that we do not blindly adhere to their authority, just as if we Catholics were not given any use of reason. So do not confuse their corrupt authority as being "The Church". I remind you that today, you are speaking about the same authority that perpetrated the new mass and all the liberal doctrines for the last 60 years - they are most assuredly not "The Church".
The excommunication of the good archbishop Lefebrve has nothing whatsoever to do with what I said - he was excommunicated for consecrating bishops. Back then, the crooks in the Vatican, including popes PVI and JP2, made him the dirty step child and repeatedly reprimanded him for his refusal to accept the new sacrilegious service and stop celebrating the True Mass.