They explained that the sharingan "copies" techniques by giving you insight into the workings of the technique, so that the mental part (the understanding part) of learning a technique is out of the way. If the technique is so simple and easy to perform that you can do it as soon as you get it, then great, you've copied it as soon as you've seen it with the sharingan. But concerning Chidori, it probably wasnt very easy to do even if you get how it's done. So it took training to master it. So yeah, I'd say he "copied" chidori. Kage bunshin...he "copied" that too I'm sure, assuming this insight ability is passive with the sharingan activated.