It is water activity. However, a low water activity level (aw) does create an osmotic imbalance.
Water activity level is a common term in microbiology and food safety. It essentially means the water that is available in the food to be used by microbes. Here is a good definition I found:
The water activity (aw) of a food is the ratio between the vapor pressure of the food itself, when in a completely undisturbed balance with the surrounding air media, and the vapor pressure of distilled water under identical conditions. A water activity of 0.80 means the vapor pressure is 80 percent of that of pure water.
It is actually one of the criteria to determine if a food is considered "potentially hazardous" (for simplicity, let's say that means it requires a controlled temperature such as refrigeration). If a food has a water activity level of below 0.85, it is considered non-potentially hazardous.
A good example of a type of food that can span the range of potentially hazardous to non-potentially hazardous is cheese. Hard cheeses such as Parmesan have water activity levels below 0.85 and do not require refrigeration. Soft cheeses such as mozzarella have a water activity level over 0.85, so they require refrigeration.
Jambs, jellys, syrups, etc. and anything with a high sugar concentration have water activity levels below 0.85 and don't require refrigeration. That's why they're on the shelf and not in the cooler at the supermarket.