If you dispute a debt from a collection agency and send it with delivery confirmation does the 30 days start from the date they received the letter?

yes. It begins when the letter is signed for. This is why it is very important to always send a letter of dispute via registered mail.

The 30 days has nothing to do with the collection agency and it's requirement to prove the validity of a debt. The 30 days applies to the consumers right to dispute a debt after receiving written notification of the debt. There is no time constraint on the collection agency to get the proof to the consumer. However, they must stop all collection activities until they do provide the proof.