True. You have to be able to control the bike, and know how to brake - preferably with pedel-brakes, which are quite common in Denmark - but otherwise with the usual handbrakes, which are on every bike.
The left wing's explanation is technically incorrect and illegal in the way it is shown. 1st the hand to signal stop should be higher not hidden by the body. It is a signal to everbody else. 2nd When turning left, it is illegal to "cross", enter over the stripes in a pedestrian crossing. Without you thinking about it you actually do it correctly yourselv towands the end when explaning how to stop when there is no obvious resin, lights, etc.
Indeed, crossing into the pedestrian zone/crossover is not legal. It can also annoy pedestrians if they are not respected and have to yield to bikes. However, in Copenhagen, there are often so many bikes making a left turn that they block the traffic at the corner (especially to the cars) if they (the bicyclists) don't 'find room' behind the pedestrian zone. So, it's common to see bikes finding their way into pedestrian zones for pragmatic reasons to make room for other bicyclists. The main message is to respect the other parties in the traffic and avoid blocking cross-overs.