This is false. There are many problems with age verification, but the EU approach does not involve the id provider in the verification flow. The site requiring verification presents a QR code which encodes a presentation request and the provider controlled URL which is to receive a presentation of the age credential, and then the smartphone generates a unique presentation signed by a device bound key and sends it to that endpoint.
It is however true that in addition to the one bit of information saying age>18, what is also revealed is the public key of the identity provider. This will at least reveal the nationality of the credential holder and - in the case there are multiple issuers within a nation - may reveal even more information about their demography.