debt validation, debt, debts, dispute form

I sent out a debt validation letter on the 17 of September, Its already the first of October and I haven't heard anything yet , do they wait until the end of the 30 days to respond? What happens if the don't respond to my letter? If I don't hear anything by the 19 of October ( that's when they received my letter) do I send out copies of my letter to the 3 credit reporting agencies to have the debt removed. Is it really this easy?
------------------------
Free Credit Dispute Form Letter
Grab the credit dispute form on the page above
Dispute accounts as not yours.