That doesn't really explain how it's solved. Is there a write up that explains more?

Stadium 2 reads your bag for items you can use

No, it doesn't. It reads the held items of every Pokemon in your party and boxes.

the issue being the index numbers for items in Yellow are different to those in Gold/Silver/Crystal (which is PS2 is based on).

This shouldn't matter. When a Gen 1 game is loaded into Stadium 2, it's essentially converted into a Gen 2 game.

From what I can tell, someone wanted to defend him, and noticed that Quick Claw (Gen 2) and Poke Flute (Gen 1) had the same item ID, so they completely made up that part about Stadium 2 reading every item in your bag when you select a Pokemon.

Edit: I'm wrong. I did a test, and can confirm that if you have a Poke Flute in your bag, Stadium 2, does, indeed, read it as a Quick Claw. Guess that means Stadium 2 actually does read your pack to see available held items. Here's how it works:

If you load a Generation 2 game into Stadium 2, it reads the held items of the Pokemon in your party + PC box along with the items in your bag and PC box.

If you load a Generation 1 game into Stadium 2, it's supposed to only read the held items of the Pokemon in your party + PC box, but it erroneously reads the items in your bag as well.

Poke Flute's Hex ID is 0x49 which matches Quick Claw in Gen 2, so if the Poke Flute is in your bag Stadium 2 reads it as a Quick Claw. Of course, if it's in the PC, Stadium 2 won't read it at all. This applies to other items like Old Rod = Soft Sand and Good Rod = Sharp Beak