There has been an event where, due to screw up - naturally - the a/c ended up depressurised at FL130. The conditions were 'a/c was depressurised above 10,000' = emergency descent.' So they, in full robotic mode, did so. Discuss.
IMHO by the time all the pax had their O2 masks on etc. etc the a/c would have been at 10,000'. Also, by the time the crew did their memory items for Cabin Depressurisation, maintaining FL130, then thought about their screw up and then put an Emergency Descent into action, they could have been calmly at 10,000' or even realised their screw up and repressurised the a/c.
Not all situations are as Black & White as the QRH would have you believe. Sadly, genuine thinking is not encouraged, or even taught, until after the event the management scream at you "what were you thinking?. You did't have to blindly do the QRH."