That's a really good point. I want to define what I think of intelligence as being so we are on the same page: it is the combination of knowledge and reason. An example of a system with high knowledge amd low reason is Wikipedia. An example of a system with high reason and low knowledge is a scientific calculator. A highly intelligent system exhibits aspects of both.
A rule based expert intelligence system can be highly intelligent, but it is not general, and maybe no arrangement of rules could make one that is general. A general intelligence system must be able to learn and adapt to foreign problems, parameters, and goals dynamically.
Yes, I think that makes sense, you can be intelligent without being generally intelligent. For some definitions the person with Alzheimer can be more intelligent than someone without, but the person without is more general intelligent thanks to ability to learn.
The classical example of a general intelligent task is to get the rules for a new game and then play it adequately, there are AI contests for that. That is easy for humans to do, games are enjoyed even by dumb people, but we have yet to make an AI that can play arbitrary games as well as even dumb humans.
Note that LLMs are more general than previous AI's thanks to in context learning, so we are making progress, but still far from as general as humans are.
A rule based expert intelligence system can be highly intelligent, but it is not general, and maybe no arrangement of rules could make one that is general. A general intelligence system must be able to learn and adapt to foreign problems, parameters, and goals dynamically.