You're comparing apples and oranges here.
If the garage advertises
Hey, we will make sure your car is full of gas
then YES, it is their responsibility to live up to their advertisement.
As the host, if you advertise that you make backups, it is your responsibility to live up to those expectations within a reasonable limit. Keeping 3 backups (daily/weekly/monthly) is NOT a 'reasonable limit'.
Yes, it is the client's responsibility to backup their own site, no questions asked, but if you, as a host claim that you make backups, then you must make every effort to make reasonable backups available... Like I said, daily/weekly/monthly is not 'reasonable', it's the lazy man's way of doing things.
Just because the industry has grown lazy doesn't mean it's acceptable.