The short version
Ratthew is a recurring character, and the collected evidence treats him as exactly that. The wiki documents a small black rat with a white snout, two buck teeth, a curled pink tail, and ears that resemble a rabbit's more than a rat's, first appearing between Shifts 2-6. No creator note and no repeatable in-game state classifies him as an anomaly, so the theory stays theory: never reject a patient because of it, and never let it change a desk verdict.