You are entirely correct, of course. There are several reasons why a flag, or anything else, might be gone quite apart from intentional destruction. This question aroused my curiosity as to why Prof Lemke thought the banners were destroyed, as opposed to some other fate. I went back and re-read his article ("Flashback", vol. 14, no. 1, p. 17) and it appears the origin of Lemke's theory was an unnamed official at the Old State House in Little Rock who responded to the inquiry about the flags. This was in about 1964. Lemke reported that this man asked him if he were "naive" enough to think a Federal flag would have been preserved by the State. The man also reportedly said that in his opinion they could not have survived the Garland administration.

Of course, the official's statements prove nothing definitive--only his opinion. Garland's accession to the governorship (mid 1870s) marked the end of the hated Reconstruction regime, and I suppose the official in question speculated that the flags would have been associated with that regime, as feelings were running pretty high in those days. This does not provide positive proof of intentional destruction--just a theory. Absent direct evidence or documentation, we simply do not know for sure what happened to them.