Correct. But why would the Russian diplomatic mission be on the senator’s campaign mailing list?
A fundraiser working for the McCain campaign, or the RNC, or one of the state parties specified in the disclaimer, purchased a commercially available mailing list that happened to contain the Russian name and address. From the story, we don't have any idea of what list the fundraiser purchased, or why the Rooskies were on it. Direct mail strategists are very creative in looking for, and testing, possible synergies. For all I know, they bought a list from the History Book Club, thinking that people who read history are disproportionately Republican, and the Russian ambassador was on it because he liked to read on WWII. That's a silly made-up example; the point is the list could have been from just about anywhere, and there are 1001 legitimate reasons the Russian ambassador might be on it.
The one thing that is certain is that the list in question was NOT a political donor list, because the Russian ambassador can't donate to an American political campaign, so he would not have been on such a list.
For what it's worth, we don't even know if this fundraiser was actually employed by any of the Republican entities mentioned above, or whether the fundraiser was an outside vendor doing contract work. (Outside contractors are very common in direct mail prospecting; housefile lists are much more valuable, and it is likelier -- though still not certain -- that a housefile mailing would be done in-house.)