Look, no. There are plenty of cases in which you can be legally defrauded without having investigated to determine whether the person you were dealing with was really telling you the truth. Retail purchases are obvious examples. Indeed, none of the commerce in which you engage holds a prospective plaintiff to the high standards of being defrauded that you think ought to hold in child-support cases. It's hard to think of other cases in which the plaintiff's action would be dismissed because there were some clues that he was being defrauded if only he had investigated thoroughly. (That's why the Rolex-in-the-alley example is not a good analogy, unless, as I've said, you think that dealing with women in relationships is typically as crooked an affair as alleyway cons!!)
For what it's worth, too, your reference to "English Common Law" is inappropriate, since historically divorce meant that the man retained custody of the children and that the woman wasn't entailed to any marital property. Illegitimate children, or "bastards" as they used to be called impolitely, weren't entitled to squat. So there aren't any "historical" standards of fraud in child-support cases(!). What we're discussing is a very recent phenomenon. It dates only back to the 1960's in America.
Finally, even if you're right about everything you're saying-- and notice I don't think you are-- there is no "balancing" issue of rights of the child versus rights of the father, as you first said. The issue is solely whether or not the father had sufficient knowledge so that he wasn't defrauded. The question, even as you're now discussing it, is not given that the father was defrauded ought we to make him pay anyway?
Reasonable investigation IF you are put on notice that something is fishy is an absolute element of ALL fraud cases. The elements of fraud are: (1) A false statement (2) Scienter (the party knows the statement is false) (3) Made with the intention of deceiving the other party (4) Reasonably relied upon by the other party (5) to the other party's damage or detriment. Item (4) requires that reliance be reasonable. Whether that's a new car salesman engaged in "puffing" (not actionable), a street seller of doubtful watches, or a woman who was pregnant when you married her telling you the baby is yours, the principle is exactly the same. Whether your reliance is reasonable is a question of fact and that varies with the facts of the case. But ALL claims for fraud have to meet the reasonable reliance standard.