Not quite true.
Under the current DirecTV DECA Cloud - No. There will be one playback list. As you scroll thru the list, it will tell which DVR it is on. Currently we can't sort the list by which DVR it is on. But that's a software issue that will probably get upgraded down-the-line if enough of customers ask for this feature.
The united playlist seem to be here to stay, though there may be some changes later. The DVR list option was here and was removed, most likely never to return.
"Managing" recording list could be thought to ask which DVR needs to record which program so they came be watched with more than one client at the same time, which would mean recording on different DVRs.