You are better off having the corporation reimburse you. For you to deduct those expenses on your personal return, there is a threshold of 2% of your Adjusted Gross Income (AGI) that you must exceed. Also, if you are close to the line between regular taxes and the Alternative Minimum Tax (AMT) you may lose the deduction entirely.
I hope this helps.
Based on additional info:
You asked: I can't understand why , if the person is the "President and Sole Shareholder" of a Corporation, how he can decide not to reimburse the business expenses and deduct them on his own tax return. It seems to me that the person is double diping. Ain't there some kind of rule, that disallows deduction on expenditure if you're a "sole shareholder"?
I'm not certain what you mean, but I'll try to get to the core of what you seem to want to know.
If the owner of the S-corp uses his car for company business and drives 500 miles, the S-corp should pay him. It can deduct the $0.55/miles ($275). This changes the shareholder's income before deductions. If this is the only expense, and the S-corp had total income of $20,000, you as the shareholder wouldn't benefit from the deduction because this type of expense requires that your total expenses exceed 2% of your Adjusted Gross Income (AGI). In this case 2% * $20,000 = $400.
If the s-corp lacks cash, you can loan the money or invest it as Additional Paid-In Capital (APIC). If the loan balance exceeds certain levels, you have to accrue interest on it. A pain, but the net to you is zero.