Experian Credit card scamming by the fraud experts , Internet

On reviewing my credit card statement there were two charts from Experian with the telephone number next to the charge. Experian offers credit reports on line to individuals.  When I talked with them they requested my credit card number and looked it up and found two individuals with accounts under my number. The gave me their first names with last letter and asked if I knew them, which I didn't and said they were reimburse the charges. $33.95 and $21.20. So I asked them how they used my card number, didn't they ask for expiration dates or security codes. He bluntly said no, that was not consumer friendly. So anyone could go on their site and fraudulently use a credit card number that is not theirs. I didn't get it. Was my card compromised. I had no other unauthorized charges.
I called my credit card company and they said they get Experian charges all the time that the company quickly returns. They were not aware of how they obtained these numbers.  Experian must successfully collect from other unintended victims or they would not continue these practices in which they are returning monies.
Anyway to get these practices shut down?