I read over here (https://aip.scitation.org/doi/pdf/10.1063/5.0040330) that "If the equi-dispersion is not met, the Poisson Regression is no longer appropriate to model the data. Moreover, the resulted model will yield biased parameter estimation and underestimate the standard error".

I have taken some intro courses in statistics and learned about "biasedness". I believe that biasedness means that the expected value of a variable subtracted from the variable itself is equal to 0.

As for the above quote, can someone please try to explain the logic behind this statement? How can we know that if equi-dispersion is not met, the Poisson Regression model will always result in biased parameter estimation and underestimate the standard error? Is this just a logical conclusion or is there actually some way to demonstrate this?