It may be that the laws of some states require that the collector must cease upon the oral request of the debtor. But the federal statute clearly imposes a requirement that the request be in writing to trigger the obligation to all cease contact. Section 805(c) of the Act states:
"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."
The debt collector cannot, however, contact the debtor at an unsual place or time (e.g. calling you a midnight) or at a time or place that the collectors knows or has reason to know is inconvienient to the debtor. See section 805(a) of the Act. Thus, if the debtor informs the collector that the debtor can't take personal calls at work, the collector is on notice that calls at work are at time or place inconvienient to the debtor and must not contact him there. This is probably the provision of the Act to which you are referring. But the scope of this is more narrow; it won't necessarily stop all communication from the collector. The written notice under § 805(c) will (if the collector follows the Act). Now, as a practical matter, it may be dificult to determine the exact reach of the prohibition of contact under § 805(a), and good business practice for a collector may be be to stop contacting the debtor once the debtor has made it clear he wants no more contact, even though the request is only oral.