I think the problem here is that you're talking to people who have been trained to think in terms of probabilities and probability trees, and furthermore, asking "what is more likely" automatically primes people to think in terms of a probability tree.

The way I originally thought about this was:

• Suppose premise 1 is true. Then two possible combinations out of three might contain a king, so 2/3 probability for a king, and since I guess we're supposed to assume that premise 1 has a 50% probability, then that means a king has a 2/6 = 1/3 probability overall. By the same logic, ace has a 2/3 probability in this branch, for a 1/3 probability overall.
• Now suppose that premise 2 is true. By the same logic as above, this branch contributes an additional 1/3 to the ace's probability mass. But this branch has no king, so the king acquires no probability mass.
• Thus the chance of an ace is 2/3 and the chance of a king is 1/3.

In other words, I interpreted the "only one of the following premises is true" as "each of these two premises has a 50% probability", to a large extent because the question of likeliness primed me to think in terms of probability trees, not logical possibilities.

Arguably, more careful thought would have suggested that possibly I shouldn't think of this as a probability tree, since you never specified the relative probabilities of the premises, and giving them some relative probability was necessary for building the probability tree. On the other hand, in informal probability puzzles, it's often common to assume that if we're picking one option out of a set of N options, then each option has a probability of 1/N unless otherwise stated. Thus, this wording is ambiguous.

In one sense, me interpreting the problem in these terms could be taken to support the claims of model theory - after all, I was focusing on only one possible model at a time, and failed to properly consider their conjunction. But on the other hand, it's also known that people tend to interpret things in the framework they've been taught to interpret them, and to use the context to guide their choice of the appropriate framework in the case of ambiguous wording. Here the context was the use of word of the "likely", guiding the choice towards the probability tree framework. So I would claim that this example alone isn't sufficient to distinguish between whether a person reading it gives the incorrect answer because of the predictions of model theory alone, or whether because the person misinterpreted the intent of the wording.