It requires the claim to be made with "willful disregard for the truth". Notifying someone, especially with a cease-and-desist on fancy letterhead, makes it legally clear that they know better, and thereafter would be definitely libelling you (assuming the claims are in fact untrue and harmful). But you can still sue them for the claim prior to the notice, you just have to prove they should have known better prior to making the claim.
Libel/defamation laws vary wildly across different countries. Sometimes true statements can be considered defamation, sometimes not. The same goes for intent.