As a result of simple syllogism, as noted in the article, some of the smarter criminals may report their income. Properly guided, they will do some without running afoul of some other tax crime (such as tax perjury, Section 7206(1), here, for misdescribing the income). But most criminals do not report the income. And then, if they are to be prosecuted for a tax crime, the Government will have to prove willfulness -- intentional violation of a known legal duty. Whether or not the Government will be able to do that is fact-dependent, but often the jury will be permitted to make the inference of willfulness and, in this type of case, may do so.
The article also suggests that, if the IRS learns of a taxpayer's income, the IRS will share it with appropriate law enforcement agencies even though prohibited by Section 6103, here. I am skeptical. I can't say it never happens, but I would be surprised if it were the routine matter claimed or suggested by the persons quoted in the article.
Finally, I would like to cut and paste the discussion in my Federal Tax Crimes book of a famous case involving this genre of issue.
In United States v. Reynolds [919 F.2d 435, 437 (7th Cir. 1990)], the taxpayer skimmed money from a public project. However, he elected to file a form 1040EZ which is supposed to be filed only by relatively low income taxpayers. The 1040EZ requested information only for wages, salaries, tips and interest. The taxpayer dutifully inserted all information requested on the return. The taxpayer did not include the skimmed income because it fit none of the categories on the form. The question was whether he could be prosecuted under § 7206(1). The Government’s theory was that by including only the information requested on the form, he implicitly represented that he had no other income. The Court responded:
The prosecutor's argument that by filing form 1040EZ a taxpayer implicitly represents that he has no additional income has more substance, but this is not the theory in the indictment. It charged that line 7, specifically, was false, and line 7 is derived arithmetically from other lines. Section 7206(1) is a perjury statute, and literal truth is a defense to perjury, even if the answer is highly misleading. Using the wrong form does not violate § 7206(1). If the form has an open-ended line calling for § 61 income, and the taxpayer leaves some income out, § 7206(1) applies. Form 1040EZ is anything but open-ended, however. The right charges are tax evasion (26 U.S.C. § 7201) and failure to supply information required by law (26 U.S.C. § 7203). Reynolds did not reveal his complete income (§ 7203) and evaded taxation on that income (§ 7201). Neither the indictment nor the charge to the jury set out the elements of these offenses, so the problem is deeper than a citation to the wrong statute in the indictment. We vacate Reynolds' tax convictions, without foreclosing indictment and trial for the offenses that match the prosecution's theory of the case.