For example, I cannot visualize a 13-sided polygon accurately, but I can draw one pretty easily without having any drawing skills.
A more realistic problem in the case of the bicycle drawing has to do with the procedural knowledge they use for drawing. For instance, maybe they approach it analytically, top-down, breaking it into major components to draw first, and those into sub components. Well, in order to do that, they need explicit knowledge of that hierarchy; they may have an accurate representation of the image somewhere, but they can't bring it directly into consciousness, and they didn't break it into that hierarchy while they had it around. So now what's left to them is to attempt to produce the hierarchy from an imperfectly recalled image, which leads to the strange configurations.
Just a guess—but I wouldn't be surprised to learn it's something on those lines.