Question

Which disease might be prevented by not sharing a water bottle?

Answer 1

Answer is cold sores!

Answer 2

C. Cold Sores. 
Cold sores aren't contagious IF you aren't having a flare up, but if you have an active cold sore on your lip, the next person to touch whatever your mouth has touched (without sanitation inbetween) will have cold sores. This is because cold sores are caused by a strain of the herpes virus, an incredibly infectious disease.
Salmonella poisoning goes from food to person and gone, if any infectious traces are left they are in your poop, and hopefully that has no water bottles involved. You aren't going to get pinkeye from sharing a water bottle either, and you sure aren't going to get a fungal infection on your feet because you shared a water bottle with someone else :P