I don't know what systemd does with HUP, but traditional inits respond to HUP by reparsing their configs, not rebooting.

In the old days, init would respond to a HUP by restarting... sort of a "warm boot." Pretty sure SunOS 4.1 did this, but ultrix certainly did. SVR 4 and Solaris changed the behaviour to just reading /etc/inittab.

Wouldn’t HUP require PID 1 to be able to process signals?

I think init still can receive signals. The only kernel ju-ju linux adds is it only delivers the signal if init has installed a handler (SIG_DFL behavior isn't triggered.)