You are right; WUBI uses the Windows bootloader which is the two line one
that first pops up. Grub will then appear afterwards. WUBI's grub is NOT
written to the bootloader of the MBR because that is where Windows'
bootloader is and only one can occupy that space. When a regular
installation is on the same computer, it will overwrite the MBR of the first
drive by default. It does not have to be there, but that is the default.
That means that you will lose the Windows bootloader if you use the Ubuntu
default and will have to work to restore WUBI as a choice. You can have more
than one grub if you have more than one drive and control which drive boots
with a boot manager. On my computer (HP) I press ESC to get a boot menu.

The purpose of WUBI's grub is to give you choice between different kernels
and boot choices in WUBI. I am not sure where that grub physically located,
but it is probably in the Ubuntu folder on the C: drive. It has been awhile
since I played around with WUBI. The purpose of the Windows bootloader is to
point you towards the two OSes installed on the C: drive, Windows and Ubuntu
which resides on the C: drive but is treated like a partition via a
loopback.

Things get very convoluted with more than one grub, but it is possible if
you know what you are doing or can at least fix mistakes manually. On my old
computer I often had three or more instances of grub. This one has only one
drive so it is fairly straightforward. Less for my brain to keep track of
which is good.