I assume the stories you are hearing resemble the tale told here.

Long story short, no, that whole story is bogus. Checking with the Oxford English Dictionary their definition for wife-beater notes that the term in reference to a shirt is an American colloquialism, and doesn't cite it in text earlier than 1993.

Furthermore, the part of the tale that says

Often, when a knight lost their armor and continued to fight successfully, they were referred to as a waif beater (waif, referring to an abandoned or lost individual)

is also incorrect. The word waif was used in medieval English to refer to lost or abandoned property or livestock. The modern meaning of a homeless or forlorn person doesn't appear in text until the late 1600s.

OED returns no results for a "waif beater".