Actually, I think you're right. It means it can burn SINs, but doesn't have to if you don't want it to.
Exactly! She can have the SIN while she wants it, but if it, or Records On File, become too much of a pain in the ass she can have Nanny Wintermute, or whatever name Kat picks, burn the SIN and the records, along with any other data that needs to be scrubbed. They go bye-bye in a day, she lays low for another week to make sure backups don't get restored, then she's off on her way with a shiny new Fake SIN purchased from Nanny.
And, just so everyone has the relevant text, here's the actual paragraph in question:
For 10 BP, any SIN, undesirable credit history, or personal information on the Matrix that she wishes is burnt (see p.96, Unwired) after 24 hours. Obviously, the eraser will preserve any data the character wishes preserved and that is vital for her to function in society.
Emphasis mine, of course.