Q:

Why is そう used to refer to something the speaker just said?

This is what I know about the こそあど words:

こ〜 is used to refer to something that is close to the speaker
そ〜 is used to refer to something that is close to the listener or something not too far away from the speaker
あ〜 is used to refer to something that is far away from both the speaker and the listener
ど〜 is used to ask questions

The use of そう here makes sense to me because it is used to refer to the thing that the listener said, which can be considered close to the listener:

A：彼の父親は医者だって。 (I heard his father is a doctor)
B：そうかもしれないな。(Yeah, he probably is)

But in the following sentence, I don't understand why そう is used instead of こう

風邪を引けばダメだ、そうでしょう？ (If you catch a cold, it will be no good. Right?)

I often hear these kind of sentences where the speaker states something then says "そうでしょう？" Obviously he/she is referring the to statement he/she just said, so why not use こう here since the words that the speaker said is considered closer to the speaker than to the listener?
Have I misunderstood completely how "closeness" work?

A:

I don't think you have misunderstood at all, but just like the distinction between "this" and "that", no textbook definition will ever exactly match.
In this case (you saying something yourself)

そうでしょう - refers to something you have already said (which is therefore in "S" territory)
こうでしょう - refers to what you are (immediately) about to say ("K" territory)

In this particular case, this is just like "this" and "that". If I claim something, I follow up with "That's right, isn't it?" but if you disagree you say "No, this is how it is."
Similarly, I might respond to your comment about catching a cold as follows:

いいえ、こうでしょう。風邪をひけば会社を休めるから、結構です。

