This anecdote probably never happened, but when John Wayne heard the story he even admitted to friends and associates that it made a great tale.It's an interesting addition to the end of the anecdote and it appears elsewhere on the net, though never -- as far as I can find -- with any original attribution. It's also interesting because it is typical of the development of apocryphal stories and urban legends that they can add a statement of comment on the traditional story, a statement that distances the teller from the story so as to inoculate the teller against charges of naiveté and provide a clear indication that the teller is smiling too. It has the effect of underlining what a great story it is that the teller has told, with self-conscious recognition of its legendary origin.
Incidentally, I have added a link to the above blurb on my Greatest Story Ever Told page. I have also updated that page with links to the DVD release. I don't own that yet, but only the VHS, so I'll get hold of it, not least because it apparently has "New documentary including on camera interviews with the director and cast" and "Original "Making Of" documentary". You can buy it second hand for a snip too. It looks like that 2 DVD set is only available in the US (Region 1) and not yet in the UK, where we just have the ordinary DVD.