(Sorry, this was to be a comment continuing on the previous thread, but I wanted to include pictures)
This picture was used in a video class I've seen, by Prof. Craig Wright from Yale where he corroborated the perspective that primite (late medieval/early renaissance context) keyboard playing was done without using the thumbs. He also referred to what he called the "3 over 3" method used afterwards until Bach's time, which seems to be the same thing as the finger crossing mentioned by Rockin above.
Another interesting source relating to this subject is Couperin's "Art of Playing the Keyboard" (L'Art the Toucher le Clavecin). This 1716 work was a reference during the Baroque and was commended by Bach himself (Christopher Hogwood, The Keyboard in Baroque Europe). Couperin stressed the use of the index, middle and ring fingers, using the thumb only occasionally in very specific situations. Here's a scale fingering from this book:
Another source that corroborates this view is the "amateur" harpsichordist (he recorded the integral Scarlatti sonatas in his custom built harpsichord!) John Sankey. His site has a wealth of information and references about ancient keyboard playing, specially the harpsichord.
Apparently this "3 finger" approach was state of the art until C.P.E.Bach's "True Art of Playing the Harpsichord", where, thumb crossing is given some relevance. Quoting from Sankey's site, «Five fingers can only play five notes in a row. To extend this range, there are two main techniques: the turning under of the thumb and the crossing over of the fingers.(C.P.E.Bach, 1753).»
I wonder if it is a coincidence that C.P.E. was among the first to write for pianoforte. I don't have any experience with the harpsichord, but I've been told it has a ligther touch than the piano, probably requiring a different technique to optimize speed and fluency. Could it be the relatively stronger touch of the new pianoforte that prompted the adoption of new techniques? Anyone can coment on this idea?