COPPA is filled with references to "websites directed towards children or with actual knowledge the data was collected from a child." Actual knowledge means you actually did know; it's OK if you honestly and unreasonably thought the child was over 13, as that means you don't have actual knowledge. To quote the FTC (emphasis added):
COPPA covers operators of general audience websites or online services only where such operators have actual knowledge that a child under age 13 is the person providing personal information. The Rule does not require operators to ask the age of visitors. However, an operator of a general audience site or service that chooses to screen its users for age in a neutral fashion may rely on the age information its users enter, even if that age information is not accurate. In some circumstances, this may mean that children are able to register on a site or service in violation of the operator’s Terms of Service. If, however, the operator later determines that a particular user is a child under age 13, COPPA’s notice and parental consent requirements will be triggered.