Yes. Banks and credit card companies both investigate disputes. They will usually contact the merchant and ask what happened and who made the purchase. The merchant will have to verify the purchase or state that it was not you.
If the merchant verifies the purpose and says there was no fraud, then the action is in the hands of the credit card company or bank. If the company knows that the purchases were unusual for you or that they were completed in a different state, they will usually give you the chargeback.