The Short Version
The underlying biology is well-supported: a kangaroo mother's teat does enlarge inside the joey's mouth and functions to keep the newborn attached during early pouch development. However, the claim simplifies a more complex process — the teat elongates, and the joey's mouth tissues form a tight seal around it, rather than the nipple merely "swelling" as if on demand. Multiple credible sources confirm the retention mechanism, though the most rigorous academic source in the evidence pool does not address this specific detail.