AW,
In the case that your accountant is talking about, the company owns the aircraft.
In the example that IO540 gives, you either own the aircraft, or hire the aircraft yourself from a third party, and charge these expenses on to the company. It's similar (if not quite the same) as charging the company a mileage rate for using your private car for work.
IO540 also adds the example that the company can also hire the aircraft from a third party and give it to you specifically for making the business related flight. Similar to a company hiring a car for a day, so that you (who doesn't have a car, but does have a drivers licence) can visit a client who is some distance away.
dp