If you summon an item using a command block (summon Item ~ ~1 ~ {Item:{id:cobblestone,count:1}} to be more exact) the item cannot be picked up, ever, even with PickupDelay set to a small number like 1 or 2, and when killing the item, the message it shows, "Killed item.tile.tilename", is wrong (screenshot attached, mine displayed item.tile.stonebrick when killing cobblestone).
Side note: The item also won't display a CustomName (MC-57516).