All the slides say is that there were 700ish reports that met case criteria as reported through VAERS, a self-reporting system. We are not told any information about which case criteria were met (objective vs subjective), comorbidities, reason for presentation (all vital information for a true diagnosis not report). We are not told about degree of hospitalisation or reason for hospitalisation. We are most certainly not given confirmed cases as GP claims, the stringent criteria for which are listed one link deep from the presentation. We are left with a misleading link to a scary-sounding number that is being posted by multiple accounts across HN with nebulous intent and in some cases history of posting blatant misinformation. I feel that calling this practice out when I see it helps if just a little bit.
In this case a look through GP's recent comment history reveals many comments with disinformation and fear-mongering.
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.
Of course I read through the link. It did not alter my reading of the slides in the slightest. The simpler tests recommended in the paper are not as objective as you might think. Again, the slides do not give us the information used and the interviews you mention did not happen for entire age categories. I'm glad you have confidence in the CDC and vaccines; GP does not and is actively trying to mislead users of HN. Appreciate the downvotes instead of discussion.
In this case a look through GP's recent comment history reveals many comments with disinformation and fear-mongering.