One always has to be suspicious of Mozilla these days.

As far as I know Mozilla never lied on technical details, at worst they didn’t know about wrongdoings by their partners and acted once known about.

The translation being done locally is advertised and should be simple to check with it being open-source. It also has to download for a while on first use, as well as translations take a considerable amount of time depending on the hardware. E.g. for larger sites it takes a short while until the last paragraph shows up as translated.