That is correct... it was whoever could grab it. D3 gives each player something, but they can immediately drop it from their inventory for someone to pick it up.
The Diablo 2 version dropped better stuff and at times. The old Diablo 3 loot system didn't drop that much - and Legendary stuff.... forget it. Legendary stuff falls a lot more frequently. Though you could argue it's not as good or whatever... even the rarer stuff that fell in the original loot system wasn't that great. It normally only fell at major bosses. Now... you could hit a pot and a legendary item could fall. I thought one fell the other day from a pot... maybe it was an enemy by the pot... but I Thought it was from the pot lol.