I was advised to not refund the customer and wait for a chargeback so that the customer will not take double my money. I was told that if I issue a refund, there is a possibility that the fraudulent customer will still place a chargeback, and therefore, would get double refunded. How could Shopify allow this. NEED THIS RESOLVED FAST. I need to know what to do with an order that is classified as a medium risk fraud. Shopify needs better security to protect its merchants in the event that this happens.
I think in your situation here, it's better to refund the customer if you feel the order is fraudulent. The Shopify fraud system is known to be inaccurate at times and it's just an indication to warn you of a possible bad order. The ultimate decision is up to you to decide whether you want to cancel or process your order. You have to weigh the benefit of either risking a chargeback, losing a potentially good customer, or just eating the cost of a potential loss.
I've written a simple article that maybe can help you with your decision making in case of a fraud order. https://medium.com/@jason_80572/five-things-you-can-look-at-to-prevent-fraud-orders-from-happening-t...
Shopify also have several articles as well to educate yourself on fraud, which you can read here, https://help.shopify.com/en/manual/payments/fraud-prevention