Much higher when you go off the vehicles electrical? That is something I have never seen... even when I had a bas @$$ voltage drop. Inverter running in my car, or someone else's car... just didnt matter. Car on, car off... no difference. I've metered an immense number of cars, and its been consistent. Its been on probably 20 different power sources... whether it be house/inverter... etc... and its always been consistent.
The only issue I've ever had was @ MECA finals when we were trying to test driveby. For whatever reason, the TL was reading over a 126 at rest. Above that it was still right on, however.
The blazer with the 12's got a .7db gain in the kick in my garage... but that was because it was in the garage. Same number sealed on the dash.
If your getting odd numbers, you need a different power inverter.