This question is answered in later arcs, so please skip this answer if you don't wish to be spoiled. Spoilers for Chapter 969, and small mention of Chapters 456, 481 (Thriller Bark Arc) and 699.
Gecko Moria did in fact steal his corpse and Shusui from his grave in Wano. As revealed in Chapter 969, this happened around a year after Roger's execution, when his old crew the Gecko Pirates clashed with Kaidou's Beast Pirates. This battle resulted in Moria's entire crew being killed, which is why he seeks a zombie crew. We see mentions of his enmity with Kaidou and his motives during the Thriller Bark arc itself, in chapters 456 and 481.
Additionally, Kin'emon gets angry in Chapter 699 because he thinks Zoro is the one who defiled Ryuma's grave. So the citizens of Wano didn't really know who did it, even though it seems they were aware of the incident.