RISC OS allowed this by design
You could set the mouse step to negative values on the Archimedes machines from BASIC, which reversed the pointer direction, and it was remembered when you returned to desktop. Great for confusing teachers or the next student. If you really wanted to upset the next user, the setting was per axis - so you could reverse one and make the other insanely sensitive without reversal.
Fixed with a reset - but 'turn it off and on again' wasn't a thing in a secondary school classroom back in 1990.