Right. Remember, they are only talking about jobs created. For instance, one summer I worked at Yale Tennis Camps for three weeks. Since I was listed as an independent contractor that was counted as a job created. It didn't matter that it was only for three weeks.
In the monthly figures they announce, sure. In the government stats for jobs held, they do go down.
I agree with your take on the monthly reports.
Hey, the same 150,000 people could have been laid off and rehired.