I can't remember hearing -san used referring to the speaker, but I have heard the diminutive -chan used in self reference. Since she is also using her given name rather than her family name, might you be mishearing san for chan?
What I have heard is the apparent use of an honorific referring to more senior member's of their family when speaking to someone I'd consider outside their group, when I would have though the humble form would be used.
tou-san rather than chichi and nee-san rather than ane.
All I can say is there is also often a mismatch between how a language comes to be spoken and how a language is described by grammarians. Languages change. You can't really say that a native Japanese doesn't know how to speak their own language. (I often dislike how some students speak English but I can't say it's not native speech. innit.
drifting off topic but there's a
nice parody here)
But as someone learning the language it's best to stick to the established rules and the rule still is you don't use san in self reference.