Essentially correct, however the MINI (both of them) have anti-knock sensors, so you'll actually cause your engine to run weaker (lower compression) automatically before you damage it because of too low octane. (In theory at least).
With regards to the original post:
Calculate the cost of super vs. regular, its at most $.20/gallon. Say you drive ~10K miles/year, which is 250/week, or about 10 gallons (assuming good milage) That's an extra $2/week on gas, or $110 a year. You just bought a car that cost over $20k. The least you could do for the poor thing is give it the gas it needs. Saving money buy decreasing the performance of your car and potentially damaging it would make sense if it was thousands of dollars. Its not.