As mentioned above, if a chargeback occurred it is because someone specificially raised the alarm: either the owner of the card alerted the bank and told them to dispute the transaction, or the bank saw something suspicious and the owner of the card said "yeah that's suspicious" and then disputed it.

Also, in the event of a chargeback, the owner of the card is given back the amount in dispute unless it's revealed everything was in perfect order. Offering to pay them back would be incredibly unwise, as they've already gotten their money back. In addition, the owner of the card is charged nothing for disputing any transaction.

The story your client is telling does not add up. Your best bet, as mentioned already, is to part ways with the client.