Well, that stopped Safari from re-opening immediately on reboot, but it doesn't prevent Safari from opening with all previously open pages once you DO open Safari. In other words, I shut down with 3 tabs in Safari, and when I reopened Safari, all 3 of those tabs with the appropriate pages opened.
This is a feature I really don't need or want. I just want to see my home page on a single tab when I open Safari. I'll open new tabs as I need them each session. I shouldn't have to close all tabs before I shut down my computer; I'm shutting it down and it should be a given that I'm done with whatever browsing I was doing at the time.
Oh, and the box in the shut down confirm window is checked again. It doesn't stay unchecked.