No, paying off debt will not increase his taxable income and should not increase the amount of taxes owed.
If he has a current year loss, it MIGHT be possible that paying off the debt could affect his ability to claim that loss, but with a corporation, I can't see how that could happen.
The only thing paying off corporate debt would affect is that it isn't paying interest, so the corporation wouldn't have that deduction for interest.
Hopefully he is just misunderstanding something. If he is doesn't understand something, he should ask the tax professional to explain it.
