The above is not precisely true. Let me present what I know, having gone through the process. It is more accurate to say you do have some choice over your core rotation site, but you should be aware that it isn't absolute. Nobody overtly makes you choose one site over another, but the rotation match process may present some limits or restrictions on your choices. That is to say, sometime during your second year, if I recall correctly, a match takes place where you list your preferences by rank order and the school attempts to match you up with one of them, typically your first choice, but there is also a lottery component because the number of slots per site is limited and varies per given site. There is a "straw poll" (or preliminary match, so to speak) before the official match, so you can get an idea of how your class is going to choose and the number of spots that are going to be taken up per site. This allows you to choose more intelligently. There are cases where students didn't heed the straw poll and ended up not matching anywhere on the first round and had to pick the left-overs because they ranked only highly popular sites, but this is rare. So you do have choice, but it's limited and you might have to make concessions. That being said, I'd say that the school tries to match you up with your first choice and you will likely get your first choice if you choose wisely. And unless things have changed, you are essentially limited to the listed affiliated core sites, which can be found on the KCUMB website, under OCCE.
There are further restrictions on the Kansas City core rotation site, because there are students in the dual DO/MBA program that are required to stay in Kansas City. They get priority/first dibs on the KC core site because of that and then there is a lottery on the remaining slots. It is likely that accommodations are made for students who must stay local, as well. Therefore, just because you list KC as your first choice in the core site match doesn't mean you will necessarily get it. You may match KC. Your probability will depend on several factors, including how many people are in the DO/MBA program. I've had classmates who wanted KC, but didn't match there and had to go elsewhere. I do not know how many KC slots there are. I imagine it varies from year to year. For my class, we had a lot of DO/MBA students, so it made the KC spots more competitive. There are other classes, I'm sure, where the KC spots were plentiful and everyone who chose it as their first choice got it. It will depend on how many spots there are and how popular it is for your given class.
I don't know. There are some additional things you should know about the KC core site. It's not just one location. If you end up matching in KC, you will end up rotating through a number of locations. You'll might be travelling to different locations monthly during your third year. Some people like this, but others do not, because it can lead to a disjointed experience, with a lack of continuity and familiarity. Other core sites do not have this situation, because for many or most of your core rotations, you are or can be at one hospital. Again, some like this and some do not. It's a preference. However, there are some advantages to doing all or the majority of your core rotations at a site where you can be at one location, more or less, because it may give you an edge for that site when it comes time for the residency match because the site knows you well and you know that site well. Keep in mind I'm just talking about your core rotations, predominately for third year, and not necessarily electives, sub-I's, or interview/audition rotations, etc., during fourth year, which you may want to schedule across different locations of your choosing to aid in the match process. Just something to think about.
This is not a complete answer, but I think it's more accurate. It's a pity that this isn't explained better at the interviews. You can't just go anywhere you dang well want, which can be an impression that some people leave with. If want to do your core rotations in Montana, for example, it's not likely to happen, because I do not believe KCUMB has any core sites there. You are essentially limited to what is on their affiliation list.
and of course get to know fellow classmates. 
