Re: This explains why ....
Grub updates are usually OK so long as you don't have a "custom" boot arrangement which you don't really understand.
That usually shows up as a prompt about what do you want the update to do, usually in terms of using the default package maintainer's config or your own (own! own!) and/or which drives to install the boot loader (MBR) on (almost a trick question as it often offers logical drives like /dev/sda1 in the list but you should only ever install on physical drives such as /dev/sda).
Also, and this is the bummer for some, most grub updates don't need a reboot. But unless you reboot there and then to test it, some weeks/months later if something is screwed up you will be forced in to booting and it borks, and you have forgotten all about this update.
So my advices is install it, if prompted keep current settings (and/or install MBR on the /dev/sda) and then do a proper clean reboot just to be sure.