Martyn,
Thanks again for this - I will check the link you sent in due course. In the meanwhile...
(a) I have exported the-model-whose-invokation-of-the-Make-Feature-Layer-tool-was-provoking-the-strange-message as a Python Script; (b) In the model that calls it, I then replaced the invokation of the model with an invokation of the exported Python script of the model; (c) I then ran the calling model.
The exported Python script version of the called model ran successfully.
Later in the same calling model, I invoke another submodel that in turn invokes the Make Feature Layer tool.
When the calling model made that invokation, the called model attempted to invoke the Make Feature Layer tool.
The attempt failed, provoking the same strange error message as I had received before.
Ideally, I'd like to get to the bottom of the strange message. Unfortunately, I don't have the time to do that.
Being pragmatic about all this, I will now be replacing all the models that call the Make Feature Layer tool with their Python script alternatives in the hope that this workaround continues to deliver satisfactory results and successful runs.
Now to reply to your last post.
The run log that my ArcMap produces when a Python script fails gives me all the information you describe.
Thanks again for your input.
