The story in Hainsworth and Church and Baumer seems to originate with John Mildmay's account

John Mildmay tells a story that Michael Baumber and Hainsworth and Churches repeat. The problem that I have with it is that no one but John Mildmay says anything about it. Besides, there are contradicting facts known to be true (about Gideon de Wildt and his ship, the Vrede). John Mildmay's story is recounted on pages 268 to 272 of The First Dutch War, Vol.II. I also looked at Colenbrander, Vol.I at John Mildmay's piece on page 24. There, he writes about Jan Jacobszoon and the frigate Gorcum. Carl Ballhausen is also referenced, but I tend to dismiss him out of hand, unless I can verify that he is correct (which he occasionally is).