They diddled their insurance company by making a false claim.

他们通过提出虚假索赔来诈骗保险公司。

《柯林斯英汉双解大词典》

But what if she genuinely believed in the false claim?

你有没有想过对方其实是真心相信她所做的陈述呢？

youdao

Someone who is moving from an interesting but false claim to a true but vacuous claim.

有人从一个有趣，但错误的宣称转移到一个真实但空虚的。

youdao

"Let's start with the false claim that illegal immigrants will get health insurance under reform,"

VOA: standard.2009.08.22

Although I guess there have been people who've made that sort of claim, it seems false to me.

尽管我想有些人,声称他们能观察到,但我对此并不苟同

耶鲁公开课 - 死亡课程节选

I think,as far as I can see,that the claim we all die alone, however we interpret it,just ends up being implausible or false.

在我看来，说我们全都会孤独而死，无论怎样解释都是不合理的，错误的。

耶鲁公开课 - 死亡课程节选

McErlean admitted making a false claim to an insurance company to claim death benefit.

BBC: Honduras 'crash death' man Anthony McErlean admits fraud

And you concluded that refuting a false claim can actually reinforce the belief in the original false statement.

NPR: Campaign Attack Ads Call 'Facts' Into Question

But his answer offers a troubling false claim about a lack of scientific consensus: the consensus is rock solid.

FORBES: Obama and Romney Talk Science. If I Worked for NASA, I'd Be Worried.