I thought that letting a VCR or DVD recorder or TV scan for channels/
stations was only to compile a list in advance of channels a device
could receive, by checking out every station and noting which had
signals.

It is.

And that pushing 1 3 on the remote would go to channel 13 whether one
had scanned for stations or not, whether digital station frequencies
had changed since the last time one scanned or not. As effectively as
if one scanned the whole spectrum, and then channeled up or down to
get to 13.

Correct. If you select a channel that hasn't been stored in the set's
scanning memory, you'll get that channel, whether or not a signal is
present.

The "go to" is instantaneous. The set does not scan from 2 through 12 before
hitting 13. The basic principle (I assume) is the same as for any digitally
tuned receiver -- the LO is directly set to the frequency needed to receive
channel 13.