No that is not true.
shutdown changes init level which then runs all the shutdown scripts. What these scripts do depends on the script. But they normally don't terminate processes but send them the signal to end.
So this is the manual excerpt for
shutdown brings the system down in a secure way. All logged-in users
are notified that the system is going down, and login(1) is blocked.
It is possible to shut the system down immediately or after a specified
delay. All processes are first notified that the system is going down
by the signal SIGTERM. This gives programs like vi(1) the time to save
the file being edited, mail and news processing programs a chance to
exit cleanly, etc. shutdown does its job by signalling the init
process, asking it to change the runlevel. Runlevel 0 is used to halt
the system, runlevel 6 is used to reboot the system, and runlevel 1 is
used to put to system into a state where administrative tasks can be
performed; this is the default if neither the -h or -r flag is given to
shutdown. To see which actions are taken on halt or reboot see the
appropriate entries for these runlevels in the file /etc/inittab.