Linear regression has two faces, that should be taught side by side:
1. A claim about nature: E(Y|x)= bx eps
2. A strategy for estimation: The best (min squared error) linear approximation of y .
The former is empirically refutable, the latter is beyond refutation.
I would say that one should also avoid teaching linear regression as
y ~ Normal(Xb, sigma)
Because that's also not what a linear regression is.
Linear regression should be taught as what it is: the best (min squared error) linear approximation of y (or of E[y|x]).