Debt collection attempts are subject to proof-of-claim. If they cannot show documentary evidence that you owe something then you can rightfully object and send them on their way. It is lawful and sensible to require them to produce validation on the account.
Although you may have viewed it merely as an application, when you opened up your credit card you signed a "promissory note" saying that you'd pay them. Original creditors will often sell that note and never notify you. Unless your state law provides otherwise, the FDCPA only requires debt collectors, not original creditors, to verify debts in certain circumstances. This includes law firms that are routinely engaged in collecting debts. If debt collectors are contacting you about your debts, you have a legal right to obtain verification of the debt.
Some people do debt validation because they are being unduly harassed by debt collectors and want to be left alone. Many learned how the banking industry operates in fraud and decide that they don't want to participate in their system any further. Regardless of your reasons, it may be good to give your credit card companies or debt collectors an opportunity to stand behind their claim.