But does a plus that happens once or twice a year outweigh minuses that happen multiple times per day?

And would the plus have even been necessary if the environment were not highly distracting? The best way to fix a bug is to prevent it from happening.

There are also other solutions to this problem, such as encouraging discussions like this to take place on something like HipChat. Now all the discussions are archived and searchable and even the people that are home sick that day have the chance to overhear something important, not just the guy that happened to be walking by.

And while yes, some discussions will still take place outside of the chat rooms, if this is your default way of working then there should be enough discussion of anything critical that everything makes it's way to chat eventually.

Once everyone's comfortable working this way you can encourage a lot more working from home (or working from wherever in the world you want to be, if your employees aren't all married with kids yet), etc. And that will save you even more on office space.

This type of "chance encounter" is a common rebuttal but instead of planning your office layout on the hope of occasionally catching a mis-communication maybe it would be better to improve how things are communicated so these "faulty assumptions" don't happen (and/or are caught sooner...independent of luck/chance).