We don't have a mathematical definition for intelligence or artificial like we do for a Turing machine, but most useful concepts don't have precise definitions, like human, air, porn, drugs, medicine. I don't see how there is anything disingenuous about calling computer programs artificially intelligent because that same term describes sci-fi computer programs which display intelligence. A lot of robots in sci-fi aren't superintelligent and they usually have robotic voices and vocabulary choices and sometimes difficulty understanding words that aren't in the dictionary or answering slightly vague questions, things which LLMs have no trouble with.

Saying the mount Rushmore carvings was formed by erosion is a simple explanation with few assumptions that is possible if you assume erosion happens sufficiently randomly, but it's an absurd explanation nonetheless. Occam's razor is just a rule of thumb to apply to competing explanations which are similarly reasonable and even then it's not telling you which is more likely to be true but which is the simplest model to work with.