When Exchanging Items Does It Have To Be a Trade?
You can give an item to another hero in your space without receiving anything in return. This FAQ from the back of the rule book clarifies this:

Q3. - If you have four items including Gasoline or Old Betsy, and you gain a fifth item, can you immediately use the Gasoline or Old Betsy to avoid having to discard an item?
A3. - Yes. You could also immediately hand off an item to any other Hero in your space.