What stops Brita filters from acting as odor absorbers?

It seems like the filter would pick up the odors from the refrigerator, and then pass them on to the water. Or no?

While I don’t know about Brita filters specifically, you can buy activated charcoal for absorbing fridge odors, so I think it’s certainly possible. However, I don’t know how well the filter remains wetted, and my hunch is that wet charcoal wouldn’t absorb odors as well as dry because I think many odor molecules are hydrophobic.