It is not wrong. In the least, it is artistic license. The worst thing about the idea of “authenticity” is the attitude of censorship it causes. Baroque music is not that restrictive. All the great harpists played the movements in this order because it is far more effective in performance, and enhances each movement.
Miss Lawrence prepared her edition from the only manuscript source, and has ornamentation that is both correctly realized and playable, unlike the Weidensaul edition. The manuscript is not in Bach’s hand, it was a copy made at a rather later date with a steel pen, so it is not absolutely authoritative. Feel free to use her edition as written. Both Grandjany and Zabaleta also played the movements in that order.
I have heard many people play it Adagio-Allegro-Allegro, and it takes all the life out of the piece in m opinion. The Zingel edition gives the original ornamentation without realization if you wish to do that yourself, but Weidensaul made mistakes, I am pretty sure, and some of her ornaments can’t be played well in tempo. I am partial, but I studied all three editions, while learning it with Miss Lawrence and we discussed them all. She spent a lot of time on it and consulted with experts. It was not lightly or sloppily thought out.
I have been preparing my own, but it is not finished as yet. It is quite difficult. I think she emphasizes the baroque qualities of the piece by using fifths and doubling the bass line. She doesn’t make it easier, but it is brilliant and dramatic. While other sonatas by Bach are in the adagio allegro allegro format, they have different kinds of music, and this is much more like, for example, the Italian Concerto of J.S. Bach, if you see it that way. Baroque music is about contrasts, and posing the adagio between allegros emphasizes the contrast of the movements. Also, given that the third movement is the longest, hearing it after the first allegro, which is much more involved and dramatic, really takes the interest out of it. Coming after the adagio, it is a lively dance and you have more leeway with the tempo. Having it after the allegro forces you to go even faster, which may not be desirable. The manuscript allows a surprising amount of flexibility in realizing it, both in terms of harmonization and voicing. (I am using the Zingel as source.)