The thing that calculates it is based on electrical resistance...something to do with muscles holding more water than fat, when combined with a weight measurement it yields an indication of body fat. I'd say it's more likely that the fluid/electrolyte balance in your body changed while you exercised (and drank water during exercise) and that would be reflected in a different reading.

Your trainer should understand that stuff otherwise it's a pretty meaningless kind of number to give you.