I found an error in the AD797 spice model provided in the standard library of LTSpice 26.
You can find this behaviour in the applications example file AD797.asc. Running this model as provided shows an 8.2mA input supply current. Which is typical according to the datasheet. This current is stable even if current is drawn from its output. I would expect the supply current to vary according to the output current. Replacing the AD797 with for example a LT1001, the error disappears. The AD797 model creates its own current to the output without a source... magic?

