Up until now, it was my understanding that multiple regression can be used to estimate the influence of an independent variable (IV) on an outcome (DV) while controlling for the influence of other possibly interfering covariates (by entering them as additional predictors; e.g., age, gender, income, etc.). Then, by looking at the coefficient of the IV of interest, I will get an impression of this variable's influence without the additional impact of the covariates (which are kept constant).
In a way, this implies a "partialling out" interpretation of multiple regression, as stated in this textbook on p. 83.
However, today I stumbled upon a recent 2020 paper (published with relatively high impact!), which claims that this is fundamentally wrong. The author claims that you should only control for so-called "confounding variables" in your regression analyses, i.e., variables that affect both the IV and the outcome. The author further explains that previous research on life satisfaction is all wrong, because it made the mistake of using "income" as a covariate in a regression between age (IV) and life satisfaction (outcome).
Could someone help me wrap my head around this? In my psychological understanding, the criticized procedure is absolutely correct: If I want to estimate the sheer influence of age on life satisfaction without the impact of another interfering variable such as money, I should keep the latter constant by adding it as a covariate, no?
Thank you very much for your help.