I didn't think to try rebooting twice.
Rebooting once, but manually choosing version 3.10 this one time, would have
been enough if I guessed right (what is not sure at all).
So, are you saying that that command writes over previous contents in the MBR
so for instance if in Fedora right now I did $ sudo update-grub, it would
write over the Trisquel grub-update result I'm using now?
As far as I understand (but I am no expert and exclusively run Trisquel):
yes.
And is it possible to install two OSes without bootloaders and depend on a
third with grub to do the os-probe and be able to configure boot up options
for all three?
I am not sure you can install an OS and not install a bootloader with it. As
far as I remember (that was more than 10 years ago), installing Windows XP
after GNU/Linux was deleting GRUB... and Windows' bootloader, which you never
see, only boots Windows. At least, that is what I understood. But, again, I
am no expert.