In many cases, the government proves this with evidence that the taxpayer deposited untaxedincome into the account, concealed his ownership of the account through sham corporations or denied having an offshore account in response to a specific question by his accountant.
At the time Obama administration was contemplating applying the same theory to Corps as to Individuals, i.e. taxed on World Wide Income, as there is a significant amount of untaxed (at least not from the US Govt) profits sitting overseas.