Question About The Jobs Report - Household Survey, The 680,000 Jobs

[Yavin4]

The Republicans are saying that the household survery is showing a net increase of 680,000 jobs in July, but the payroll survey from the corporations is only showing 32,000 jobs created in July. So, why the discrepancy? Here's my theory. Please tell me if it's accurate or not:

My Theory:

Because the job market has been miserable for four years running, people are more likely to take real short term temp work, even if it's a day or two. So, let's say Jane Doe takes a three day temp assignment. She won't show up on the payroll of the company that used her services, and she may not show up on the payroll of the temp company. However, when she gets called by the BLS, she shows up as having a job because if you work during a two or three week window around the phone survey, you are counted as employed.