“According to that logic”
its not a logic
its a mashul
mashalim, of course, always have some logic as there is a comparison between the mushal and the nimshal
but it can range from a very loose comparison to a very tight comparison (less to more “logic”)
it is NEVER exact because then the mashul would be absorbed into the nimshal and they would be one
i think you understand the point of this particular mushal