The problem I tried is below. You need to know that GZP is not a book of life & death but rather a book of boundary-play problems. Although L&D aspects can crop up, you are actually meant to be concerned with eking out extra profit, which you can do in various way - cutting off tails, fattening the slaughtered calf, encroaching, and so on. A tesuji (or two, or three - this is a hard book) is generally required rather than mere counting.
It is White to move, and a throw-in A makes a profitable capture. He cuts off the tail. But he can do better by fattening the calf.
With the position as shown, Lizzie gave the correct first move A (according to the original and backed by Go Seigen et al.), as below:
Lizzie also gave the correct follow-up as Black B. And then plumped for White C (after B was actually played). But the humans believe White D is the correct move.
I tried a variant position in which the rest of the board was filled up with absolutely secure territory for both sides, so that the only plays left were in the problem position. That altered Lizzie's perception but just seemed to make things worse initially. However, she did find the right answer after a few minutes.
That seems to suggest to me that bots can't be trusted in such positions unless you allow them to play slowly (much as for humans, I suppose
The full human solution here is embedded in the position below.