You seem very confused. At first I was worried you misunderstood my text: maybe you have trouble with natural language but not programming (or maybe English but not code). That would certainly explain your claim that they are disjoint skillsets. But as you went on, you committed a logic error, so now I'm just thrown.

There is a difference between "find the errors in this provided code" and "write code on a whiteboard with no errors". At no point was I talking about code you wrote.

Also, it's an aside, but I find people who can program well write excellent documentation for the users, if what they are writing is an API. Of course, they are not the best at explaining the steps in a GUI, but that probably has less to do with communication skills in general and more to do with the difficulty understanding how they perceive the problem.