I can confirm this happens -
-I added an ID of human, then added another ID of human (which withdraws the first ID). I refreshed the page to ensure that the checkbox for “Mark as Reviewed” in the lower right corner was checked.
-I deleted my first, withdrawn ID of human
-The observation is now not marked as reviewed, even though I have an active ID on the observation
I edited the title of your bug report to reflect this unexpected behavior.
You could also try using the URL parameter ident_user_id in the meantime: https://www.inaturalist.org/observations?place_id=any&subview=table&taxon_id=48548&verifiable=any&ident_user_id=nycbirder
and see also this open feature request for better identification searching tools: https://forum.inaturalist.org/t/search-and-filter-identifications/1304