I have seen photographs of a mouse suspended in a red back web before. Red back venom is extremely toxic and their silk is extremely strong. The mouse probably blundered into the web and the red back quickly secured it with more silk. Killing the mouse would have required repeated bites because the fangs are fairly small.
However, the huntsman builds no web and although the fangs are large, the venom is weak. I rather think that spider on the fridge happened upon an already dead mouse and decided it was food. If it was smart, it would have secreted the mouse under the fridge and waited for the flies to find it. It would have been guaranteed fresh food for about a fortnight.