We play that you must always take an Item (even if you decide not to keep it) before taking a event when using the Supply option. This came up when Hunters had reached their hand limit, were happy with their Items and just wanted the Event card.
I think this is covered in the FAQ but wanted to make sure.
I can't see it mentioned in the FAQ, but it seems clear from the supply action entry on the back page of the reference guide.
.. If in a large city, draw an item card
before drawing an event card.
It does not say you may draw an item, so it is compulsory.
There is a more detailed reference to the supply action within the reference guide, but that makes no mention of it being optional either.