I remember a discussion about them in a presentation some time back, and some mention that at least some of the known coins were scattered in early bags of the Philadelphia coins and a few were in 1964 proof sets. If so, it certainly wouldn't be
impossible for one to be found in the wild.
There are also other markers to identify one of these coins. On the obverse, there are a couple very small die gouges in the hair near the "B" of LIBERTY and a die scratch between WE and TRUST. On the reverse, there are die scratches from the bottom left of the N in UNITED to the star beneath the U of UNITED, inside the second S of STATES, and a longer scratch connecting the top of that S to the bottom of the O in OF.
Back in the day, I had a chance to see in hand one of the Denver (1964-D) presentation pieces. It looked less like the Philadelphia 1964 SMS coin, but more like a semi-prooflike
Morgan dollar (to use the old phrase). It, too, was clearly different than the regular business strikes. Denver selected two regular working dies, basined them specially, and double or triple struck the presentation pieces for "dignitaries."
Are the Philadelphia coins remainders from a similar striking? If so, where are the rest? Were they kept by the "dignitaries" or were they spent?