Kilian doesn't share a tone of details but he did post word of the rescue on his blog. He does say that they were carrying the necessary climbing gear with them as they went up the mountain but they were traveling in a minimal amount of gear. As a result, when the weather took a turn for the worse, they didn't have warm enough clothes with them. Fortunately that didn't prove to be a fatal mistake but it easily could have gone that way if a few variables had gone badly.
There are certainly a few lessons to be learned from this story, not the least of which is that the mountains should always be respected. Over the past couple of years we've watched in awe as Kilian has done some very impressive things on numerous mountains across Europe and elsewhere. He has always looked confident and in control no matter where he has gone and his incredible athletic ability has made given him an aura of invincibility. This incident proves that no matter who you are the mountains can provide a humbling experience.
The other thing to take away from this is that while we all want to be able to travel light and fast it is important to remember that you don't go so light that you're leaving important gear behind at home. Kilian and Emelie would have faced less difficult had they carried an extra jacket with them when they hit the trail. Something that they probably should have had in their packs specifically for these "just in case" moments.
Thankfully no one was seriously injured in this situation and Kilian did the right thing by calling for assistance when he did. Hopefully he'll use a little better judgment the next time he heads out into the mountains and hopefully we all can learn a little something from the incident as well.