And most of the people working in those industries are actually putting anything together. They are accounts, sales reps, office people, etc. Do their numbers count as being in the "manufacturing sector?"
Yes. They do. Ford is a manufacturing company and yet the majority of the employees are white collar. It's typical for most industries. The numbers of small company manufacturers here is staggering. Even in the Seattle area. I work with several small sheet metal shops, crane manufacturers, electrical specialty shops....and that's just the stuff dedicated to a small segment of our economy. Small companies also tend to be light on overhead and heavy on production.