One problem I have had with dealing with Google (not for this particular service) is that they set up mechanisms where adding a "backup" creates a new single point of failure rather than adding redundancy. If you can't access one particular backup method of verification, your primary and other backup are of no use. It's a trap! And quite Kafkaesque.

While this might not strictly apply to some other particular situation, my experience would lead me not to ever trust Google when they say "do this seemingly logical thing because it will make you safer".