They really screwed up when designing the push button phones. They reversed the order of the numbers compared to adding machines.
It was deliberate.
People skilled with data entry could push the buttons MUCH faster than the switching system could keep up. The equipment needed enough time to discriminate between which of the three column tones AND which of the four row tones were intended before the next number was pressed.
There simply weren't tone detectors and other electronics available at the time to do this over noisy and lower quality lines.
Flipping the top and bottom rows slowed down the 10,000 numbers entry per hour accountants...