No: hide it for all players.
Then show it for the local player only.
Something like this: (editor not open, I hope it'll work
).
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Hide "Reviver_Display"
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Custom script: if GetLocalPlayer() == GetTriggerPlayer()
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Show Reviver_Display
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Custom script: endif
In case you're using a specific unit event (instead of a generic one), it should be "if GetLocalPlayer == GetOwningPlayer(GetTriggerUnit())".