The logic is simple. Suppose that a fast programmer can do some task in time t. We have a slow programmer who programs twice as slowly. In the worst case all of time t spent by the fast programmer was spent programming which is what the slow guy is slow at. In that case our slow programmer will take 2t, a linear amount of time. If the slow programmer had an alternative strategy he would only use it if it reduced the time to complete the task. Therefore the time is linear at worst.

Note that even if the slow guy is 1000 times slower it's still linear.

Please explain why the logic isn't right. Could it be that the logic is right but that slow programmers tend to do things on paper first, which is not the best strategy?