A computer's master boot record consists of raw binary and does not reside on any sort of partition. Legacy GRUB and GRUB 2 are installed to the sectors inbetween the end of the MBR and the start of the first partition. The boot code in the MBR, which is blind to filesystem formatting, loads GRUB from the no man's land residing after it. Why are the MBR (boot.img) and GRUB (core.img) accessible as files through the Linux filesystem?
First, in linux, everything is a file. Binaries and libs are all files.
Second, boot.img and core.img are not in your MBR. The MBR is the first part of your hard drive and contains the initial boot and partition table. The MBR then passes off the boot process to grub, which is located on your boot partition.
See
https://wiki.archlinux.org/index.php/Master_Boot_Record
http://www.thegeekstuff.com/2011/02/linux-boot-process/
https://www.gnu.org/software/grub/manual/html_node/Images.html
From the last link
and
both boot.img and core.img are a part of the grub package and are stored in /boot, regardless as to if /boot is a separate partition from / or not