What is probably happening is that the employer is taking a distribution from the company of money on which he (the employer) has already paid the tax. Then he is giving it to his employee. Hence, he is telling the employee that the tax on the money has already been paid (it was taxed as corporate or partnership profit to the shareholders or partners).
In the employer's mind, the tax has been paid and he is treating the check to his employee almost as a gift, which it could be if it were not given in return for any services rendered.
As to why employers would do this, consider that the employer is not paying his share of FICA and Medicare, nor is he paying Fed and State unemployment tax. Depending on the employer's tax bracket (which could be zero if there is a large amount of deductions or a NOL on his return) he, the employer, could actually be saving money.
I do not agree with the employer nor would I take the client unless he reported all of the checks as income.