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In the getEBPCaseDetail response below, you see that the caseSummary.status is "Paid" while the caseDetail.detailStatusInfo.description is closed. Is "Paid" also a type of "close"?
You can use caseDetail.detailStatusInfo to determine the most recent status of a case. As documented, caseDetail.detailStatusInfo can be considered as the high-level status of the case. As a result, this case has indeed been closed as per detailStatusInfo showing here:
<description>The escalated case has been closed by eBay.</description>
The reason the case in the <EBPINRStatus>PAID</EBPINRStatus> status is that a REFUND was paid to the buyer as showing in the paymentDetail container as below: