Contact both the customer and BBB to clarify the complaint and confirm it was intended for you.

You can delight both parties by accepting responsibility and expressing empathy, even if you are not at fault.

There is a long-told customer service story about Nordstrom accepting an faulty car tire because the customer claimed she bought it here. Turns out, the site used to house a tire shop prior to Nordstom moving in.

To your success,
-Shaun