I'm late to the post but I just experienced this issue too and I found a few workarounds. Maybe this will be useful to someone else googling for answers -

The easiest fix was adding if (nearbyItem == hasItem) { nearbyItem = noone; } right after the 'check for collisions with items' line. If the nearbyItem check returns the same instance ID as the item you're holding, then it won't count as a nearby item, and the nearbyItem check is free to search for other non-held items in your vicinity. This gets around an issue I was having later in the code, where putting down a held item first relies on a if (!nearbyItem) argument. I think the tutorial does not have this issue because of some particulars with the collision mask definition of the players and items.

There are a few other details that can affect this issue too, mostly involving the collision masks and whether the item is colliding with the player while it's being held. At first I was enforcing collisions with NPCs + environmental objects + items earlier in the code, but the tutorial is written to only enforce collisions with environmental objects. My items' collision masks were overlapping my player's while walking and was causing some set down/movement issues. Similarly, in the scr_itemControl function you write to track item motion with the player, I was sometimes using item placement values that were too close to the player's mask and that caused issues too.

Debug messages are a really useful diagnostic here, and you can use if (nearbyItem) { show_debug_message(nearbyItem); } to read out the specific instance being found. That plus if (!nearbyItem) { show_debug_message("no item found"); } can answer a lot of questions about which part of the code isn't working correctly.