Take a look at Halleck's message to Meade which accompanied Lincoln's order to take command, and you'll see for yourself who used the "invading forces of the rebels" language first.
You will also find in that message the edict mentioned by Eric Wittenberg to "cover the capital and also Baltimore". (OR Vol 27, Part I, pg. 61).
In addition to Eric's book, I would also highly recommend a piece by A. Wilson Greene, entitled "From Gettysburg to Falling Waters", which can be found in Gallagher's book The Third Day & Beyond, for details on Meade's pursuit.
Greene did a great job of summarizing the critiques of Meade in the historiography of the campaign, and then effectively dismantled them, one by one.
i think that if you study the dispatches between Meade and Halleck(and Lincoln) you will find that Halleck was, personally, perfectly satisfied with Meade's pursuit. It was Lincoln who was dissatisfied. The dispatches praising Meade's efforst, were usually Halleck himself; when calling for more speed and aggression, it was Halleck passing along Lincoln's instructions.
It is true, that until Grant, it seemed beyond the capacity of Union generals to wrap their minds around the concept of Protecting Washington(and.or Baltimore) by closing with the ANV and force Lee's attention on what the AoP might do to him and Richmond, do that, and the defense of Washington and Baltimore is moot. It certainly was beyond Meade's frame of reference, i.e., he seemed to believe he could only do one or the other and not both.
Early in my studies, i was always provoked by the study of Meade's pursuit, as I have studied it more, I have reached the conclusion, already expressed, that given the state of Meade's mind and temper and that of his senior commanders, little could be reasonably expected from his trying to attack the ANV and probably would have been distinctly unpleasant for the AoP.