They did reply to Mr Stoller
https://aspe.hhs.gov/cdc-%E2%80%94-influenza-deaths-hhs-response-rfc
They admit to mixing numbers but say it's not misleading.
"CDC thinks it is important to convey the full burden of influenza to the public. Thus, we do not agree that it is misleading to combine direct deaths associated with influenza with those likely associated with secondary pneumonia and estimates of those likely associated exacerbations of underlying chronic conditions"