Does it depend much on the corporate structure of this company?
Is it a small company? More specifically, is it, say, a single proprietorship, and is this Big Boss the top-dog CEO, President, owner of the company? Is it his company, to fire and hire at will on-the-spot like that?
Is there even a HR department at all at this company?
If it’s a large enough company to have a HR department, then probably no boss of any level can just, at his own initiative, fire anybody on-the-spot like that. It would necessarily have to follow some process, go through HR, paperwork, the works. There would be checks and balances.
What does it mean for the bigwig to fire him on the spot? Does he just say “you’re fired”, Trump style, and that’s it? Is such a summary, verbal firing even effective? What if the hero employee just quietly shows up for work the following day?
ETA: Re-reading the OP: His hypothesis, “your department is being visited by a company bigwig”, implies that this is, in fact, a large enough company to have departments, and bigwigs who aren’t always there (i.e., there’s a “corporate headquarters” somewhere else in the building, or not even in the same building), so there’s certainly going to be a HR department to work through. I don’t think even a bigwig can fire anybody on the spot like that. He might be able to demand that the employee be fired, but it still has to go through some HR process, and there would be more eyes than just Mr. Bigwig’s reviewing the proceedings.