Actually, that's a 9th Circuit case ... Ohio is in the 6th Circuit. This case is not binding on Ohio.
And there can be any number of reasons under which the officer impounded the vehicle. And, even if in the 9th Circuit, the car could have still been taken if the community caretaking element could be articulated. In this case, it could be that the officer could articulate that had the vehicle not been towed it was very likely to have continued to have been driven on the street or some similar argument.
Bottom line is that your car was towed. You had best make some phone calls and find out how to get it out of impound as soon as possible or those daily fees will start to rack up!
Sorry.

