I follow the same line of thinking. And while the fruit was in the body, it underwent some fundamental change so that when it passed from the body, it corrupted, the soil, which corrupted the plants, which in turn corrupted every living thing, leading to death. Mere forbidden fruit falling to the ground caused no such problem.
Romans 5:12 Therefore, just as sin entered the world through one man, and death through sin...
Romans 8:21 that the creation itself will be liberated from its bondage to decay and brought into the freedom and glory of the children of God.
Just to clarify, the preceding explanation the DNA mechanism of corruption and death is pure conjecture.