The fake part isn't whether differential privacy exists. The fake part is claiming differential privacy can be used by browsers to provide aggregate ad conversion data to advertising networks without providing information that can be linked to an individual.
According to Mozilla[1], Firefox's implementaion uses the "Distributed Aggregation Protocol" (DAP)[2]. Individual browsers report their behavior to a data aggregation server, which in turn reports aggregate data to an advertiser's server using differential privacy. But the aggregation server still knows the behavior of individual browsers, so basically it's a semantic trick to claim the advertiser can't infer the behvior of individual users by defining part of the advertising network to not be the advertiser.
Now, Mozilla says the data aggregation server they use is run by the Internet Security Research Group[3], which is a non-profit, so perhaps the social incentives truely are aligned in this case to ensure individual user behavior isn't shared with advertisers. But it's disingenuous to claim user privacy is protected absolutely by technical measures when in reality it's only protected by social measures.
Finally, ad conversions can easily be measured without cookies by serving unique URLs with each ad, so what's even the point of this technology? I'm not clever enough to discern any ulterior motives (if there even are any), but the complexity of the approach is suspicious to me, since ostensibly a much more obvious solution would suffice.
[1]: https://support.mozilla.org/en-US/kb/privacy-preserving-attr...
[2]: https://datatracker.ietf.org/doc/html/draft-ietf-ppm-dap
[3]: https://en.wikipedia.org/wiki/Internet_Security_Research_Gro...