To be fair, its hard to say what the sharingan is capable of copying anymore. Kishimoto himself seems to have forgotten how the sharingan derived its name. Based on the original explanation both every character with the sharingan should have a multitude of techniques that they have never shown in combat. As it stands now, it is really hard to know what the sharingan is capable of copying because Kishimoto has basically ignored the sharingan's copying abilities for the majority of the series.
Personally, I would agree that it would be common sense to assume that Kakashi could perform the hidden mist technique based on how easily he copied other techniques early on it the series. However, it is difficult to say for certain because the Hidden Mist technique was basically used to block his sharingan, so it is difficult to say whether he was able to copy it. With that said though, we know that Kakashi can copy techniques and has copied over 1000 techniques. We haven't seen him use nearly that many so for someone to say that he cannot use it just because it hasn't been shown is if anything more baseless than to say that he definitely can't use it. We have to assume that most characters with the sharingan have more techniques than the show and simply choose not to use them because that is the nature of the sharingan. Notice that in most battles Itachi doesn't use water techniques at all but we know that he can use them and he has probably copied most of Kisame's because that is how the sharingan has been defined to work. Another example is Nagato, in the manga he is almost never shown using elemental techniques at all but we have been told that he can use every element and could learn every technique he was shown easily. Based on that I would say it is safe to assume that he can use most of the common water, earth, fire, and wind techniques.
So to answer the question, I would say, it is true that we cannot say for sure that Kakashi can use the hidden mist technique but based on the sharingan's ability to copy techniques and the fact that Kakashi seemed to copy all of Zabuza and Kisame's other water techniques with ease, it is not unreasonable to assume that he was able to copy the hidden mist technique. Also we have been told that he has copied 1000 techniques and well over 90% of those haven't been shown, so saying that because he hasn't been shown using it he must not have it, is an invalid argument. Kakashi likely doesn't use the technique because in most situations it doesn't support his fighting style. Kakashi relies heavily on his sharingan and keen vision, so using the hidden mist technique would impair many of his greatest strengths. In the case of Zabuza the hidden mist technique suited his skill set very well because he had excellent hearing and relied mostly on sneak attacks.