Wrong, deaths that happen after COVID infections are not necceseraly considered COVID deaths.
You are probably considering the CDC's preliminary numbers, whicha re all people who died while infected with covid at all, vs its final numbers (which lag by a few months) that indicate people who die of COVID specifically.
Often the media, as they do tend to dial the fear up, use the preliminary numbers as a scare tactic without being honest about what they mean.
Long and short of it, despite the misinformation in the general public the actual statistical data does **not** work the way you just described.