I agree with most of what you say here, especially the bit I’ve highlighted, but there was an example earlier in the game that disproves this.
Walker went down in an innocuous challenge and managed to roll umpteen times - almost rolling off the pitch (“get up you twat. Clearly not injured”). He had treatment, went off the pitch, came back on, (“I knew it. Not injured at all”). Minutes later went down injured again, substituted, (“maybe injured after all”). Replays showed him catching his standing foot as he went to clear the ball. Injured, but capable of rolling.