Clarkson created the persona. He was developing it during the first, cancelled, run of Top Gear and then obviously perfected it during the second which, as people who think you should be allowed to punch colleagues never seem to tire of saying, he owned the rights to.
I'm quite prepared to believe that what's on screen is exaggerated, not least because it seems to be a fairly commonly repeated claim, but the creation is his own.
So was he sending someone to A&E because he couldn't get steak in character or would it have been worse if he'd been exaggerating for the cameras?
Perhaps to avoid confusion he should have chosen a different name for his TG character? I've often thought him akin to Al Murray's pub landlord character; Al says far more outrageous things than Clarkson ever has but seldom comes under attack.
(To avoid confusion and outraging the easily outraged this is no endorsement of punching work colleagues )