It is not possible in classic for a single install to determine who needs to loot a corpse. The information on retail is only available from the tooltip, so with that line gone from classic, we're blind. It is possible to query if a corpse is yours with CanLootUnit(unit), but in order for a whole party to figure out who "owns" the corpse, an addon or weakaura querying that function has to be installed by everyone.
If you intend on making that and can get a whole group to install it, the way Blizzard uses it on retail suggests the return won't work immediately after a mob death, you have to delay it by at least 1 second. The relevant usage is in retail's tutorial code:
From my observations, the only times a loot item is tinted red is either you're in a group with master looter on or the mob dropped a quest item that you already have enough of to complete the objective. Loot intended for other people simply doesn't show up in classic.