larryd:
There is no Ground on a battery. "Ground" is an arbitrary concept. Yes, there are cases where the Ground Point is defined, such as on the Arduino [which defines it as the Negative Side of the Voltage Source], but the positive side of a battery can, also, be chosen as "Ground" [have you never heard of a positive ground car?]. Thus, the Circuit Designer as full freedom to place "Ground" wherever he/she chooses. For instance, there are OpAmps, such as the LM324, that are designed to function with a single rail supply, in which case, the inverting input is tied to the negative side of the supply--a side that assumes an identity as "Ground". But, such OpAmps, usually, can function just fine with a dual rail supply. In which case the moniker "Ground" is assigned to the point halfway between the Positive, and Negative supply points.
In my schematic there is the pre-defined Arduino "Ground" [which may, or may not, be connected to the actual physical ground]. And, the MOSFET Drain circuit, has it's own "Common" that is connected to the Arduino's 3V pin, and to the Positive side of the battery -- neither of which is ground [i.e. the *ground* defined by the Arduino].
And, therein lies the source of the confusion: conflating the concept of "Ground", with the concept of "Common". I agree there should be only one "Ground", in the sense that a true Ground is actually connected to the physical ground [i.e. the *Earth*], and there's only one "Earth". But, there can be more than one common, which is the case in this schematic of mine [the one that has raised so much alarm], and connecting two unrelated commons to ground, will likely lead to a short. But, why would anybody do that -- noobs included? It's not part of the schematic -- the schematic clearly shows how things are to be connected.
And, so often, the term "Ground" is used, when it's really a "Common" -- like in the case of the Arduino [where is an Arduino connected to the Earth?!?] It's like how we still say, "The phone is ringing", when, really, its a cellphone playing "We are the champions!". Back in the day, Ground actually meant, It's connected to the Earth.