This is a hard one to answer.
While we're required to disclose the SSN for the child care credit or FSA, does the IRS match it against anything? In theory, that's the purpose, but in practice, it doesn't appear to be part of the IRS' matching process currently.
The problem is, we can't tell kids NOT to report their income. Legally, if they meet the requirements to file a tax return, they are required to report their income regardless of how or if it's reported.