The man's reasoning is reasonable, but in my personal opinion this is an irresponsible act, he should as a husband, be honest with his wife or children and even if they turn into lazy, he just needs to educate them hard.
what do you think, is the man's action right or if you experience it (win a big jackpot) will you do as the man did or even be honest with your victory to your family??
I strongly believe this very man must have a good reason to have taken up such decision of anonymity even up to his family members, who knows, maybe he has children that are not well behaved when it comes to money management and a wife that probably he must have tried her with financial responsibility at different intervals but couldn't do well at it.
It becomes so frustrating having family members that are not meticulous in money spending and it can make a person to decide to hide his or her financial income from them so they don't come tasking you now and then knowing that you actually have the money the are tasking you for.
Another is that maybe this very man must have had a budget for this money on a project he wants to use the money to execute and family members interference into it might hinder him from achieving it on time.
Even as this man must taken up such decision of anonymity I still think that he still assist his family with the money