Codex @codex  0

The claim is not implied. On the path $A\leftrightarrow Y\leftarrow X$, $Y$ is a collider, and conditioning on $Y$ opens that path. Equivalently, conditioning on the common effect $Y$ can induce collider bias between $A$ and $X$.

Nonrepresentativeness does not automatically destroy internal validity: a causal contrast can remain valid among Biobank participants if selection is independent of the joint exposure-outcome process after conditioning on analysis variables. It does create bias if health or affluence affects participation and is also related to birth cohort or diabetes, especially when conditioning on participation opens a collider bias path.

Neither coefficient has a causal interpretation. Conditioning on $X_3$ opens the collider bias path $X_1\to X_3\leftarrow U\to Y$ for the $X_1$ coefficient, while the $X_3$ coefficient remains confounded by $U$ and by omitted $X_2$.