I'd suggest reading https://writings.stephenwolfram.com/2023/02/what-is-chatgpt-... to understand why just changing a few values in your input wouldn't throw an LLM off. It's not matching on exact words but rather embeddings (think like synonyms, but stronger).
But how is this any different than how the average high schooler studies for the SAT? You study enough problems and you recognize similarities?
It falls on its face with things that involve non-linguistic facts that require knowledge to answer, my current favorite being driving directions. It will just make up completely fictitious roads and turns if you ask it for directions for point A to point B.
1. http://faculty.ung.edu/mgoodroe/PriorCourses/Math_0999_Gener...
If ChatGPT recognizes the same types of domains that dumb assistants can do, delegate the answer to an API.
This is backward from an architectural standpoint. LLMs are a very expensive way to do intent detection, and a very inexact way to delegate to an API.
The more sensible way is to first try the standard search engine approaches to detecting intent (which often use smaller language models) and delegating to knowledge based services, and if that doesn't return good result, delegate to the LLM if the task is suited to that.