privacy is the main reason. corporations can not steal/sell your private data if customers are not giving them the private data. giving the data is not necessity with bitcoin.
I don't think giving fiat money gives data at all. They don't have the power to trace each serial number of the money only the government can. Also giving fiat money no matter what denomination it is is not an effective research for the business/company as every money does not have only one owner it can be money from someones change.
He probably means with credit cards, because as you said paying with fiat if you are paying cash no one would be able to steal any personal data of yours but maybe if some nasty shop keepers or markets steal your private data when you pay with credit card if they find your balance reasonable which is not possible to be done with bitcoins.