Why connect two power supply grounds?
Voltage is not an absolute value. It's pointless to say they're grounds and therefore are the same. It's like suggesting that I'm five miles away from New York and you're nine miles, therefore I just need to walk four miles to get to you. Except it's even worse than that, because that's a reference point, it's more like saying I'm five miles from my destination and you're nine miles from your destination. Are we near each other? We don't know unless our destination is the same place. Ground is just a name for your arbitrary point of reference.

For your voltages, all you have is a reference to a different point. Ground does not inherently mean 0V with reference to any other thing you want to call ground. Call your left thumb ground, a perfectly valid thing to do, and see if that makes sense to you. 

So the ground on the battery and the ground on the Arduino could be quite different if referenced to one another or to a different point. The only way you can be sure you have a system with 5V and 9V supplies is if they have a common reference point.