Hawkeye1974,
Because of so called iconographic evidence (pictures to most of us) that appear to, and indeed do, show English archers using bows with recurved tips and also because of the exposure of the English archers to Burgundian bows, which did have recurved, tips, and, as has been suggested, with a recurve the performance is likely to be better, there are people who argue that the English Bow therefore must have been recureved as its unlikely that they would let such an "improvement" go to waste. The truth of the matter is there may have been recurved bows used in England but on the whole there is no evidence of recurves being widespread.
As for why would someone from the Mary Rose Trust agree, well you may have been watching a program in which two like minded individuals were taking part.
**EDIT** having looked at the program, at least in part I think you need to have another look at the part where you said the Mary Rose bloke agreed, The man in question is or was the keeper of the artifacts, the Collections Manger, he is/was probably not an expert in the bows. I did not see him agreeing nor disagreeing in fact he was not in the shot when the claim about recurved tips was made.
I have no idea if tests have been done with bows at warbow weights to see if heat bent recurves will stay in ir will pull out, perhaps someone who has will let us know the result?
Craig.