I don't know what Monika saw in CS 5 but she must have ungrouped the graph by accident

here is a screen shot of a chart in CS as it is when first generated

If I ungroup it which make it no longer a live Graph

I gaet what the op shows,

Same exact behavior in CS 6 nothing has been done to the Graph feature though it is hopeful that it might be next time.

You can file a bug report but Adobe engineers will not be able to reproduce it as you describe.

You either accidentallyor unconscously ungroup the graph o0therwise you cannot rearrange the order of the groups within the graaph group.

You can move elements of the graph with the direct select tool but if you access the data and make a change that change an all the moved elements will reflect what is in the data and will return to those coordinates.

They retain any new strokes or effects but the data recorded is always reflected as per the entered data when you click the apply button until you break the group. As the Op clearly is showing in their screenshot.

I am not discredting anyone just saying that you have accidentally ungrouped the object which is what you are doing when you direct select the object within the graph and move it outside the group

Here see for yourself. I seelcted the red plot element oj the canvas and I moved it to the only place it can be moved above the graph. Now of course when I select the graph it is no longer part of the graph only the plot points sre which I did not move.

If I then go bnack to the graphs data what i does is makes a new copy of from the data all you do my dragging the element outside the group ius to essentially make a copy of it  that is not linked to the data

You accidentally ungrouped it.

And let's get something straight when someone points out that i made a mistake i don't accused them of ill will of anykind I accept my error
and thank the other user for pointing it out, that is how we learn and that is what the forum is about learning we all learn.

So you might want to apologize for falsely accusing me of something did not do or intend to do.

In Cs 6 the work around would be to amke a new layer select the elements from the graph than paste in place in the new layer.

Or if you wan it in the same layer as the graph then copy paste in place .

I don't think this is a bug although some users might want this to work that wy.