My own opinion is that the provision you are referring to (which comes from Section 3C of the Immigration Act 1971 and is often called "Section 3C leave") only relates to applications for a variation of "leave to remain".
An application for a Residence Card is not an application for leave to remain under the Immigration Rules. So Section 3C cannot apply.
Interestingly, Chen parents
are provided for under the Immigraiton Rules, so the way I read it, a hypothetical Tier 1 migrant could benefit from Section 3C leave if they were applying to remain as the parent of a self-sufficient EEA child. Weird.
But in the thread I linked to earlier, the OP got similar advice to yours from the UKBA in the same situation. If their policy is to treat EEA applicants as if they were making an application to vary leave (and thus allow them to benefit from Section 3C) then that would be great
In some policy documents the UKBA does provide for discretion to be exercised so that people using the EEA route are not disadvantaged unfairly when it comes to the application of the Immigration Rules (for instance, last time I checked, someone with a Residence Card as a spouse can apply for leave to remain for access to a child in the UK, without having to fulfil the technical condition that they currently have a spouse visa), so it would be nice if the UKBA took that view here too.