After reading the datasheet, this is how I interpret the switch states of the ADG788 analog switch:
This interpretation is based on the "Truth table" in the datasheet:
Nevertheless, it feels a bit counter-intuitive. It is weird that the B-poles are connected when the inputs are 0. Wouldn't it be more "intuitive" if the A-poles would be connected at input zero?
Yes, your interpretation of the ADG788 operation is correct.
Good point for your comment about the SxA and SxB (A/B-poles as you mentioned) ON/OFF states. However, I would think logic inputs are most probably referenced with respect to the first switch (SxA or A-poles). So when logic input is low, the initial concern is to turn-OFF the first switch (SxA), so this means turning-ON the second switch (SxB) as this is an SPDT. This also goes when logic input is high so the first switch (SxA) is to be turned-ON and second switch (SxB) is turned-OFF.
Hope this helps.