IELTS band scores compared to CPE

On the Exam English home page the comparison chart indicates that CPE is euivalent to IELTS band 7.5.
This is based on documents published by IELTS and the British Council, but are they correct?

Please refer to the Cambridge ESOL Research Notes : Issue 19 /February 2005/pages 19-24 - on Figure 4 : Comparisons of IELTS, CSW and CEFR bands where they note that \"High IELTS performance bands 8 and the top Band 9 appear to be the level of C2, CPE. Indications from the study are also that CSW level 5 (CEFR C2) stretches from high IELTS Band 8 to 9."

I am seeking clarification from Cambridge ESOL

Thank you to the Exam English visitor who pointed this out.