I don't think that's true. There is no source of information in-game that says the short sword pierces defense.
go and read the items stats in the game data the attack that the sickle uses adds def into the comparison sicklenormal adds +2 atk and +2 def to the comparison while shortsword adds +5 atk and +2 def to the comparison which could be more easily be expressed as
Sickle = atk+0 and shortsword = atk+3
the files are sicklenormal and shortswordnormal
which is to say the sickle does less damage just in general but its only like 2 atk worth of damage