Any profits from offshore companies, owned, directly and/or indirectly, or simply controlled are also taxable. Even companies registered under someone else's name, for example, a strawman, trustee or relative. In the latter case, not disclosing that these companies are actually yours it's a crime under U.S. Law and you might got to jail for tax evasion and money laundering.
Remember that in the US, tax evasion convictions require only a jury's veredict, strict documentary proof is not necessary.
