The car lost power because it went into limp mode. The DME picked up something out of tolerance and reduced power to save the engine. If you stopped straight away, then everything would be fine, the fan stays on even when the car is switched off.
When my wifes 323i water pump failed it did so on the highway in summer. We literally drove the car in limp mode straight to BMW Alberante about 20kms. There was no damage to the engine at all. The car now has over 261 000kms on it without any side effects from driving with the failed pump. These engines are a lot stronger than people think.
If the water pump went then the thermostat stays in an open position to allow some water to flow. Your fan would then go crazy load at max speed to cool the engine down as well. If you stopped straight away, then everything would be fine, the fan stays on even when the car is switched off.
But if you really do want to keep the car and want to have piece of mind, I would say get everything and I mean everything in writing, absolutely no exceptions.