Putting gas in the employee's car is taxable to the employee. They are "throwing money at them" for something that cannot be proven. There is no way to state you split a tank of gas. That's why the Mileage Allowance method works. What you have is personal use of company resources, which is either to be repaid by the employee (and then they would turn in mileage) or taxable to the employee, because money is always taxable (runs through payroll).

Their intentions are fine, but there is a reason the IRS uses the phrase "An Accountable Plan." It's not Reimbursement. It's just more money.