Yes it's very wrong to have batteries and some other voltage source connected in parallel - just think about all those warnings about not putting normal batteries in a battery charger and that should suffice.
So to give a unit 2 options of power source, as mentioned the power sources have to be somehow switched between, whether it's a plug with switching capabilities or just an added toggle switch that routes one source at a time to the unit.
As for measuring a higher voltage on a transformer than is written on the label, that is an unregulated power supply and it will read higher when it's unloaded, but when you use it to power something, it should drop down to more around the expected level. Try putting the meter on it when it's plugged into whatever it was designed for. Unregulated supplies are used either when the target device has a voltage regulator to stabilize it, or when the exact voltage doesn't matter.