The the FSA will be added back to your taxable income.
The FSA trustee is supposed to use due diligence to make sure they are only reimbursing legitimate expenses. I don't know exactly what that entails from the IRS point of view.
But you must report the provider's name, address and tax ID number on your tax return or you can't claim the dependent care credit or the FSA benefit. The IRS uses that information to match to the providers' tax return and make sure they are reporting the income and paying taxes. Or you can indicate the provider refused, in which case you can't e-file, and you have to provide a written explanation that will probably lead to an audit for the provider.
The provider does not have to give you their personal SSN. They can get an EIN (business tax number) from the IRS to report their business income and give out to clients, the process is free and takes about 15 minutes online.
