What utter nonsense. Winter tyres will often increase the braking distance when the conditions aren't bad enough. Unless it's full on icy the all season will probably brake in a shorter distance than the winter. All season tyres may be slightly less pliable than winters but they also remain flexibility under 7 degrees.
They don't know what they're on about. It's not the sidewall flexibility, it's the tread blocks. Winter tyres have deeper grooves and sipes in the blocks so they squirm around. All season tyres tend to have some sipes but less than winters.
Ignore them and fit CrossClimate.
Watch this.