When you read back you will notice that I've never said the dog will not react to commands. That is pure invention on your part. What I have said and which follows on perfectly logically from the professiional dog handler's comment is that the dog will not sense that it is in "work mode". Dogs are conditioned to work mode by various means. In the case of a guide dog that might well be the putting on of a harness. In the case of other dogs that might be related to uniform. The dog may be in more playful mode and more easily distracted when not given familiar cues such as the uniform which the professional handler tells us is important.
No, no he doesn't say it's important. He doesn't say that at all. That is YOU saying that. Did you watch the nice vid I posted earlier of Mr Grime in and out of his jumper while training his dogs?
As I'm sure you noticed, it didn't affect the dog's alerts. Do you know why? It was because the dog is trained, probably on a particular word to do a particular thing.
Should the trainer have been wearing his 'dog training clothes' the dog would have known it was going out for training at an earlier point. it is the command that the dog reacts to, not the clothing, not the environment, not the weather. The command.