That's exactly what that person is "implying", and that person is correct. But with the caveat that this applies much more to things like infotainment than to things like engine control. Lots of car software is purchased off the shelf and then customized slightly for branding purposes. But obviously some manufacturers do write their own software. For instance, as far as I'm aware, Tesla's software is all written in house (someone can correct me if I'm wrong here).

I worked for a company that provided such software to auto manufacturers, and I assume we had competitors, so yes.