The story about the twins being raised by a prostitute (whose name was Acca Larentia, by the way) was already well-known in Roman times.
> Sunt qui Larentiam volgato corpore lupam inter pastores vocatam putent; inde locum fabulae ac miraculo datum.
> Some writers think that Larentia, from her unchaste life, had got the nickname of "She-wolf" amongst the shepherds, and that this was the origin of the marvellous story.
(Titus Livius, Ab Urbe Condita, I.4)
Probably, people just kept using the legend of the she-wolf to symbolize the might of Rome.
