No that's not a good summary.

The model can only reason from the weights directly when there's a fairly linear relationship between the behaviour and the weight values. In a large model that's not remotely true.

Using Python to debug and fix problems with the model is totally different. It doesn't read in any of the weight values into the context at all when it uses the Python approach. Rather it gathers diagnostic statistics about the weights. It does just the same sort of thing a machine learning researcher would do to solve the problem.

So there are basically two unrelated types of experiments in the paper. In one type of experiment, the model reads the weights like it reads an image. In fact if you visualise the weights it's fairly clear why this works.

In the other type of experiment, the model is tasked with writing Python code to do ML engineering. This requires writing Python programs to analyse and manipulate weight data. This is a difficult coding problem but it really is just a coding problem. It doesn't "look" at the weights in these tasks any more than you or I would look at the weights.