I would say as long as it is stated you can complete the coding exercise using any tool available it is fine. I do agree, no task should be a trick.
I am personally of the view you should be able to use search engines, AI, anything you want, as the task should be representative of doing the task in person. The key focus has to be the programmer's knowledge and why they did what they did.
One client of mine has a couple repositories for non-mission critical things like their fork of an open source project, decommissioned microservices, a SVG generator for their web front-end, etc.
They also take this approach of "whatever tool works," but their coding test is "here's some symptoms of the SVG generator misbehaving, figure out what happened and fix it," which requires digging into the commit history, issues, actually looking at the SVG output, etc.
Once you've figured out how the system architecture works, and the most likely component to be causing the problem, you have to convert part of the code to use a newer, undocumented API exposed by a RPC server that speaks a serialization format that no LLM has ever seen before. Doing this is actually way faster and accurate using an AI, if you know how to centaur with it and make sure the output is tested to be correct.
This is a much more representative test of how someone's going to handle doing actual work knocking issues out.
I am personally of the view you should be able to use search engines, AI, anything you want, as the task should be representative of doing the task in person. The key focus has to be the programmer's knowledge and why they did what they did.