The answer is, for better or worse, “it depends.” As explained elsewhere in the Q&A section, IRC Section 7201 makes it a crime to “willfully attempt in any manner to evade or defeat” a tax. Accordingly, one of the main things the government must prove beyond a reasonable doubt is that you acted willfully. Proof of willfulness is required in all criminal tax cases. U.S. v. Moran, 493 F.3d 1002 (9th Cir. 2007). Someone acts willfully in violating a statute when he voluntary, intentionally violates a known legal duty. U.S. v. Pomponio, 429 U.S. 10 (1976).
Suppose a taxpayer maintains he is innocent in filing a false return because he relied on his accountant. Will this get him off the liability hook? In such cases, the issue comes down to whether the taxpayer knew when he signed the return that it was false. The court will infer that he acted willfully in filing the false return if he (1) was aware of the contents in the tax return, and (2) he knew that his actual income was significantly more than the amount reported. Thus, the answer to the original question turns on whether the government can prove these two things.