Read the Fair Debt Collection Act. You can find it here:
http://www4.law.cornell.edu/uscode/15/ch41.html#PC41 subchapter V, sec. 1692.
Write them again, and mention 15 U.S.C. sec. 1692c & 1692e. Instruct them not to contact you further, as you refuse to pay the debt because it is invalid.
Sec. 1692c
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(c) Ceasing communication
If a consumer notifies a debt collector in writing that the consumer refuses to pay a debt or that the consumer wishes the debt collector to cease further communication with the consumer, the debt collector shall not communicate further with the consumer with respect to such debt, except -
(1) to advise the consumer that the debt collector's further efforts are being terminated;
(2) to notify the consumer that the debt collector or creditor may invoke specified remedies which are ordinarily invoked by such debt collector or creditor; or
(3) where applicable, to notify the consumer that the debt collector or creditor intends to invoke a specified remedy. If such notice from the consumer is made by mail, notification shall be complete upon receipt.
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Sec. 1692k. Civil liability
(a) Amount of damages
Except as otherwise provided by this section, any debt collector who fails to comply with any provision of this subchapter with respect to any person is liable to such person in an amount equal to the sum of -
(1) any actual damage sustained by such person as a result of such failure;
(2) (A) in the case of any action by an individual, such additional damages as the court may allow, but not exceeding $1,000; or ...
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This is not legal advice and you are not my client. Double check everything with your own attorney and your state's laws.