Until the IRS says that it has adopted a special definition of non willfulness.....

Willful blindness for purposes of the income tax and the FATCA willful penalty does not include gross negligence or its parallel recklessness.
Willful blindness goes by various labels, such as specific intent, willful ignorance, deliberate ignorance, conscious avoidance, etc. For most tax crimes and the FBAR crimes, willfulness -- defined as specific intent to violate a known legal duty -- is required.  Ignorance is an excuse.  In the context of tax crimes requiring willfulness, the willful blindness construct says that, if a trier of fact is otherwise unable to find the requisite specific intent for willfulness, the trier may consider the fact that the defendant deliberately acted in a way to be – or appear to be – ignorant of the facts or the law applicable to the facts and treat that real or feigned ignorance as either (a) the equivalent of the specific intent required or (b) an inference of the specific intent which, with the other evidence, will permit the trier to find the required specific intent beyond a reasonable doubt.  (willful blindness is not the equivalent of specific intent.)  In either event, if permitted, it can lead to a conviction of a crime requiring specific intent where the evidence might otherwise be insufficient for the trier to find the requisite specific intent.  In the FBAR civil penalty context, the willful blindness concept can permit the application of the FBAR willful civil penalty.  The current IRS definition of NW conduct is conduct that is due to negligence, inadvertence, or mistake or conduct that is the result of a good faith misunderstanding of the requirements of the law....This definition seems to be incomplete.

If anything less than the statutorily required  specific intent can be willful this would expand the scope of the criminal statute or civil penalty by judicial interpretation......to find the required specific intent to the required level -- beyond a reasonable doubt in criminal cases and either preponderance or clear and convincing in a civil case. In a tax case, the language of any conscious avoidance instruction must not conflict with the government’s obligation to prove the voluntary, intentional violation of a known legal duty. See § 8.08. Care must be taken to ensure that the conscious avoidance instruction applies only to the element of "knowledge" and does not extend to the government's obligation to prove a "voluntary, intentional violation." When a deliberate ignorance or conscious avoidance instruction is given, the jury should also be given a separate Good Faith instruction, which expressly directs the jury not to convict for negligence or mistake. A showing of mistake, negligence, carelessness, recklessness, or even gross negligence is not sufficient to support a finding of either willfulness or knowledge.
Certainly, recklessness is a concept similar to gross negligence and is not willful blindness which requires, not reckless, not negligent, even grossly negligent, but deliberate conduct at least to avoid knowledge.
So, if a taxpayer reasonable believes that his conduct is gross negligence (or recklessness) -- but not willful blindness -- at worst, can he certify nonwillfulness?  Currently it appears this way. Conduct showing only gross negligence (or recklessness) but not specific intent nor deliberate avoidance of specific intent will not establish willfulness or permit willfulness to be inferred. 

In the Williams case, the appellate court said that
Thus, we are convinced that, at a minimum, Williams’s undisputed actions establish reckless conduct, which satisfies the proof requirement under § 5314. Safeco Ins., 551 U.S. at 57.
Accordingly, we conclude that the district court clearly erred in finding that willfulness had not been established.
And that came after the Global Tech SC decision. So at least in the 4th Circuit, case law seems to be that recklessness suffices to indicate willfulness in the FBAR penalty contest.

http://federaltaxcrimes.blogspot.ch/2014/07/yesterday-i-wrote-blog-titled-willful.html