"One-day" delivery, NOT "next-day"....
...so as long as they deliver it "one day"....they will have hit their promise.
If the had said "next-day" or "next business day" then that would have been a different matter.
I guess if they delivered an order across more than one day (ie multiple consignments over more than one day), then that might get them in hot water too.
Ho hum..