How is a modern digital oscilloscope calibrated?
The verification process, I assume, is exactly the same

That is a wrong assumption, to have a person sit down and calibrate a scope like this is too expensive. It can be automated ! I bet the manufacturers have an automated bench for this, just connect signals to the input and control the scope using a PC. Feed it +1.000 V DC, measure the "raw number" which the scope's ADC measures. Then feed it -1.000 VDC, measure again. Then program the scope such that +1.000 V gives +1.000V on the screen. After the ADC it is just numbers so the calibration can be done in software.

The same is done in a modern digital multimeter. All the pots are gone, calibration is done in software and stored in a flash ROM.

Time calibration is also not needed on digital scopes as they use a quartz crystal which will always be miles ahead regarding accuracy compared to analog scopes using an RC sawtooth generator circuit (for the horizontal deflection).

On an analog CRT based scope, the spot where the electron beam hits the screen must be calibrated (X, Y position). On a digital scope, there's a an LCD display, each pixel can be adressed individually by the application processor. No need to calibrate.