Contaminated tattoo needles is another documented way to get Hep C. It can also happen with piercings. Anything where an instrument is used to pierce the skin, is a potential source for infection with blood-born conditions. Licensed operators are supposed to follow strict sterilization procedures, and most do, but there will always be some who cut corners. And then of course there are the unlicensed and "do it yourself" situations.
So while COM has no way to know if the story is true or not, it is definitely a known source, which is why the doctor accepted the story.