The “former statement” is:
Davenport admitted that his results were normally effected [that is, they were tricks, not genuine spiritual phenomena]
And the “latter statement” is:
the instruments never left the cabinet
So Doyle’s argument seems to be that since the latter statement is wrong, then Houdini must have misquoted or misunderstoood Ira Davenport, and if he could get one statement wrong, he could do the same for another. But it is Doyle who has misread or misremembered his sources, for Houdini did not quote Ira Davenport as saying, “the instruments never left the cabinet”, but rather:
the musical instruments never left our hands
Ira Davenport, quoted in Harry Houdini (1924). A Magician Among The Spirits, p. 25. New York: Harper.
I think what must have happened is that Doyle, who never saw the Davenport brothers give a performance (William Davenport died in 1877, when Doyle was just eighteen), had to rely on accounts written by gullible spectators, and in his imagination he conflated elements of two different types of performance into one impossible version.
The Davenport brothers seem to have given at least two types of performance, one in which the effects were hidden from the spectators by the closed doors of their cabinet, and another in which the effects were hidden by darkness. Houdini quotes a newspaper description of a typical “dark” performance thus:
“The musical instruments, bells, etc., were placed on the table; the Brothers Davenport were then manacled, hands and feet, and securely bound to the chairs by ropes. A chain of communication (though not a circular one) was formed, and the instant the lights were extinguished the musical instruments appeared to be carried all about the room. The current of air, which they occasioned in their rapid transit was felt upon the faces of all present.
“The bells were loudly rung; the trumpets made knocks upon the floor, and the tambourine appeared running around the room, jingling with all its might. At the same time sparks were observed as if passing from South to West. Several persons exclaimed that they were touched by the instruments, which on one occasion became so demonstrative that one gentleman received a knock on the nasal organ which broke the skin and caused a few drops of blood to flow.”
Houdini, p. 25.
Houdini says that this report is from the London Post, but the British Newspaper Archive shows that it was syndicated and appeared in various newspapers, including the Sun for Thursday 29 September 1864.
It should be clear that in the dark, the man who was struck on the nose could not have known what kind of object he had been struck with, and although Doyle imagines it to be a floating guitar, we are not compelled to agree with him. Houdini writes:
After I finished reading [the newspaper report] Ira exclaimed:
“Strange how people imagine things in the dark! Why, the musical instruments never left our hands yet many spectators would have taken an oath that they heard them flying over their heads.” *
* As to the delusion of sound. Sound waves are deflected just as light waves are reflected by the intervention of a proper medium and under certain conditions it is a difficult thing to locate their source. Stuart Cumberland told me an interesting test to prove the inability of a blindfolded person to trace sound to its source. It is exceedingly simple; merely clicking two coins over the head of the blindfolded person.
Houdini, pp. 25–26.
Magicians are well aware of this tendency for people to conflate two different performances of an effect into a single version combining features of both, calling it “cancelling methods” because each performance can “cancel” a different theory about how the trick is done.