Ok, this is a bit technical, but the way the game works seems to be as follows:
--Player1 plays a singleplayer world, and opens it to LAN
--Player2 joins and collects some stuff
--Both players quit
--Player2 loads up the single player world, and the "singleplayer inventory," stored in the level.dat file, is loaded and OVERWRITES Player2's inventory from the last session.
--Player1 joins and keeps their same inventory
--So basically, Player1's inventory has been duplicated and Player2's inventory has been deleted.

It's true, few players will run into this situation, but it has been a thorn in my side with all the tinkering I do, and would still be worth looking into! At least have a menu pop up that says something like, "Load Player2 LAN Inventory or keep Singleplayer Inventory?" Of course, if it's a player who hasn't been on the map before it could skip the menu.