Employment Law Questions? Ask an Employment Lawyer.
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Employers are not legally required to offer paid holidays at all and so they can set their own rules with regard to how and when those days are administered. Unless there is an unlawful discriminatory basis for denying a particular employee a holiday day (i.e. their race, religion or gender), it is permissible to deny the day. Denying a paid holiday because the employee is already off that day would not be an unlawful discriminatory reason for denying the day.
In short, how your employer chooses to handle this situation is purely up to them. The fair thing would be to still pay you for the day, and you can certainly try to convince them of that if they don't agree with you initially. But you cannot legally force them to pay you for a day you do not work, or to allow you to take a different day as your holiday.
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