As it's a bootloader, it should make almost no difference which distribution was used to install it. (I'm not sure if Debian patches their GRUB.) I just used Arch as an example, as it is famous for being up to date. And, no matter where it's installed from, if you've made changes to GRUB's configuration, you'll have to copy it over to the live distribution to keep your changes.
Yes, Debian Sid might be more familiar for Debian users, but that's it.
Edit: You said "get the grub debs from Debian sid", but installing Sid packages on non-Sid systems isn't something that you should do.