No, this isn't the claim.

EU wants Apple to open 'Siri AI', with access to a personal context, open to other model/AI providers.

Apple says "We can't do this in a privacy preserving way".

You can definitely question what their true motivations are, but it seems pretty plausible that there is a moral case for this system to not be opened up to other providers who may do a worse job at privacy than Apple (especially when you are Apple and you trust yourself).

I think there is a place in these sorts of ecosystems for privileged players. If you buy an iPhone you implicitly must trust Apple to some degree.