It should be safe to reply "Yes" to that question, as long as you didn't change the part in the new assembly.
Another alternative would be to close the assembly before opening the drawing. It will probably be able to find the appropriate saved part. If it doesn't, you can probably point it to the right part.
Even when I click "Yes" the drawing references the part that is inside the assembly and not the part file its self. But they are the same part. So the dims are in the wrong place and tons of different errors. Even when the dialogue box gives me the option to find the correct reference file, it still says that it will not work or "does not match the internal ID saved with the referencing document" and the ID (or name of the part file) is the same as the 2D drawing.
It makes sense that answering "Yes" when the assembly is open will leave the drawing referencing the part in the assembly; that's what you told it to do.
I don't know why you would have errors if the part truly did not change when you stored it inside the assembly. I suspect that it must have been modified in some way.
If it still tells you that the internal ID is incorrect when you point it at another file, that makes me think that you are still not pointing at the correct (the original) file. One trick is that accepting a new file (by saying "Yes" and then saving the drawing) resets the internal ID, so it will now think that the original file is not correct.
The internal ID is a hidden value that only SolidWorks knows. It has nothing to do with the name of the part file.