Does the link https://www.cdc.gov/mmwr/volumes/70/wr/pdfs/mm7027e2-H.pdf on the same page 11 answer your concerns? That paper (from June) explains in some details what the CDC did, and I would assume that the slides are just an update of the numbers on the paper to a later date. At least the author of the slides was an author of the paper, so I would infer that they kept doing whatever they were doing in June.
One thing that the paper is pretty clear about is that in order to proclaim a "case", the CDC reviewed medical records and interviewed the healthcare provider looking for specific criteria. It seems like all criteria include at least one test, e.g. EKG, in addition to symptoms reported by the patient. It's not like they ran a SQL query over a bunch of dudes reporting chest pain---the CDC did their homework. If anything, I have more confidence in the CDC and the vaccines now than I had before reading these documents.