The given /etc/init.d script indicates it should be stopped at one of the runlevels 0, 1, or 6 but not at all of them. This is usually a mistake. Normally, facilities that need to be stopped at any of those runlevels need to be stopped at all of them.
For example, if it is safe for the facility provided by this init script to be stopped by sendsigs at runlevels 0 and 6, there should be no reason to special case runlevel 1, where killprocs would stop it. If the facility needs special shutdown handling when rebooting the system (runlevel 6), it probably needs the same handling when halting the system (runlevel 0) or switching to single-user mode (runlevel 1).