Have not been here for a while so am only joining this discussion now:
With regard to non yew bows on the Mary Rose: the Mary Rose Trust's artifact data base:
http://www.maryrose.org/database/mary_rose_archive.htmllists all bows as being made of yew except for:
Artifact No. 79A0471 which is stated as being a 320 mm piece of a
willow bow. See record No. 2425;
Artifact No. 81A0213 which is stated as being a 102 mm piece of a bow of unspecified wood. See record 2426;
Plus two bows that were used in tests and had horn nocks fitted so in the column where on other bows they state yew or indeed in the one case willow, they state "Horn: Wood:" see record No. 2322, artifact No. 81A1607 and record No. 2411 artifact No. 81A3975.
Therefore unless their data base is wrong, it seems there is one piece of wood that is thought to be from a willow bow and one unidentified piece all the remainder are claimed to be of yew. AS this claimed willow bow piece is only 320 mm long one can understand the reluctance of people to speak of it especially as it is not of a recognised "English" bow wood.
Regarding flat bows, I have not seen the bows but from my reading of the various books etc on the subject of the Mary Rose bows I believe that what is meant by references to flat bows are actually squarish sectioned bows.
Craig.