All of those points are true, but there’s one I’d like to flag as true but potentially misleading:
Linear regression assumes a linear relationship
Linear regression does assume this in that it tries to find the optimal linear combination of predictors to represent a dependent variable. However, there’s nothing stopping a researcher from feeding in e.g. x and x squared as predictors, and thereby finding the best quadratic relationship between x and some dependent variable.
The general advice here is
Not all regression is the same; beware anyone who reports doing “a regression”
Linear regression assumes a linear relationship
Don’t trust a report that bases its authority on numbers if you can’t say what those numbers mean
A conclusion can be both true and misleading
A little unreflective folk-psychology (“vitamins” as being “more is better” instead of having a dose-response curve) can do a lot of damage
All of those points are true, but there’s one I’d like to flag as true but potentially misleading:
Linear regression does assume this in that it tries to find the optimal linear combination of predictors to represent a dependent variable. However, there’s nothing stopping a researcher from feeding in e.g. x and x squared as predictors, and thereby finding the best quadratic relationship between x and some dependent variable.