Leaving this here in case someone else with an MSI product gets the same issue.
I contacted MSI because the solution of reflashing the BIOS suggested by Brio wasn't working.
And they told me they have the fix at https://www.msi.com/faq/faq-11370
I followed the steps and it worked. No more Secure Boot problems. Now I have to see if the laptop keeps shutting down or not...