This is not necessarily implausible.
I do agree that a lot of flu cases are probably being misclassified as Covid-19, be it out of caution, malice, or whatever.
That aside, let's try and explain this. The most important value for the spread of a disease is the reproduction number (R0), meaning the number of people someone with the disease infects on average. It's a way to express how infectious a disease is.
If the R0 value was 2 for a disease, the amount of people infected grows over time, as for every person infected, two more get the disease.
If the R0 is was 0.5, only one new infection would happen for every two ongoing cases.
Covids R0 was initially reported as 2.9 but is likely to be even higher.
Influenza R0 is around 1.5 for most strains.
That is, if you do nothing to prevent the spread.
If you introduced measures to cut the infection rate in half for both diseases, for example, the infection rate for Covid would still be 1.5, meaning the number of infections goes up on average.
Meanwhile the Influenza R0 would below 1 at about 0.75, meaning it would slowly disappear as fewer people get infected over time.