NEC ECC: Acceptance of CE quotation and subsequent realisation it was not a CE!

Contractor issued EWN related to ground conditions. PM requested a quotation which was submitted by Contractor and subsequently accepted by the PM.

Following a review by the Clients team, it was found that the information related to the ground conditions had been issued to the Contractor and included within contract appendices.  Therefore, Contractor has recovered costs through Activity Schedule and  Compensation Event.

 My thoughts were
1.    The CE decision has been implemented. My understanding is that, under NEC3, such a decision can then only be challenged by adjudication (and, ultimately arbitration)
2.    Any dispute under NEC3 can usually only be referred to adjudication if notice is given within 4 weeks of the dispute becoming apparent
3.    It is slightly difficult to see how the Employer can raise an adjudication challenging its own decision
4.    It may be possible to re-visit this in the final account?
5.    Still worth raising the point with the Contractor at this stage - there is an outside chance they will agree the CE decision was incorrect

Is there a way out of this situation considering the above?