Asivad is right - for any program you apply for through EE, your IELTS must be valid both when you make your EE profile and when you SUBMIT your application. In our case, our IELTS expired three weeks after we got our ITA. We were not able to submit our PR application by then because it took some time to get our medical appointment, so we had to retake and submit the new IELTS results with our PR application. But if we had been able to turn in the PR application before the IELTS expired, we would have been fine.
It is unclear what the quote you supplied means by "application process" - is it just when you are applying for EE, or when your application is being evaluated? But their other quote - the one that says specifically it must be valid when you make your profile and when you turn in your PR application is very clear, and no one on this board has reported being rejected because they met that requirement, but their IELTS expired before getting PR.