Q about flash exposure compensation

As English is not my native language, there is something I want to check.

Mr. Friedman says something about flash-compensation (A77/65) that is not quite clear to me, so I want to rephrase it and ask you if I am right about this.

Page 257

Usually when you set flash-compensation to say -1, the picture is 1 step underexposed.

When set the exposure compensation to ambient only, the picture is correctly exposed, but the flash gives 1 step less light than it would usually do.

To me only the latter makes sense as every camera has the exposure compensation button to compensate exposure for the picture.

Correct me if I am wrong.

Thanks for looking at my question.

Peter