I have to agree that if they are in the open and have no sign, they are fair game. And I think it would be tacky to have a sign. Of course, we don't allow food out on desks, so all of ours would be in the kitchen/lunchroom where everyone shares.
I think someone needs to remember their Kindergarten rules about sharing. Honestly, if my employees were bickering about something so unproductive, I would probably ban all snack-sharing.
This reminds me of a story.....Years ago, a group of consultants were at the main corporate office of a very large discount retailer (VLDR). There was a problem with the system the consultants worked on and it caused both the consultants and employees of the VLDR to work late. The VLDR ordered pizza for their employees and told the consultants that if they were hungry, they could get a candy bar out of the vending machine. They did NOT share their pizza. Personally I still think this was tacky and a bad business practice and still leaves a bad memory. But it wasn't the only bad business practice of this VLDR and is one of the many reasons I haven't visited the VLDR in over 6 years.