It was as simple as taking ownership of C:\ProgramData\Malwarebytes. The Installation was successful this time, and I am currently running a full system scan. Is this safe? Should I "remove ownership" after?
No need.
Good news
I thought you removed Malwarebytes folder from there before and you took ownership of ProgramData before.
Oh I know what happened... Ownership applies to files only so if needed any subfolder have to be taken care of separately.