Amazingly it seems my theory could have some corroborating evidence:

1. Firstly I hear word that St Petrocs the Padstow Church has in its East Window - behind the High Altar a depiction of a canopy with bow, arrow, sword and two peculiar hunting horns which is a badge representing St. Petroc, the first Abbot and founder of Padstow church. And the bow? It's a reflex recurve and not a longbow!!! St Petroc the saint of Cornwall is symbolised with a reflex recurve.

2. Then I'm told that in Cotehele - the National Trust house in Cornwall on the wall are hung two unstrung reflexes! These would look odd to anyone not in the know about bows as unstrung they look like this:

and when strung like this:

When I was told this I had a dim memory of seeing an unstrung Reflex in Buckfast Abbey - but I'll need to go there to prove my finding.

But so far it looks like the history books and the Cornish archery society are wrong and indeed the Cornish used recurves and not long bows.