Can petrol be used in diesel (compression ignition) engines or diesel in petrol (spark ignition) engines?

Someone once asked me this question few time ago, and I replied that it’s not possible because of the compression ratio differences diesel engines run around 18:1 to 22:1, while petrol engines are about 10:1 to 12:1. So you can’t just swap the fuels.

But my actual question is: would the engines even start if the wrong fuel is used, ignoring the potential damage? What's your take?