Ah, this took me a while to figure out! At first I thought it was the file size or the spacing of the rivets.
But I'm 99% sure what you see is because you have doubled lines, using the line tool rather than a single pen line. Basically you've drawn long rectangles and the brush wants to put rivets on both sides, not straight down the middle. I believe they look stagared because of something to do with where the box/line starts and ends. The path strokes at one end and goes around to the other end. If you use single lines, not the line tool, you wont see this I think. You'll notice the circle and square look ok.
Basically, use the pen tool to draw a single line and don't use the line tool.
Here is the real problem, what to do if you want the line tool to use for another part of you project and don't want to do the lines twice? Not sure if it's possible.
Does this answer your question or do want more detail?