Well, Italy is quite (in)famous for their mafia... Well, anyway, what's with not having "la" before "mia"? Is it because that's only required when the possessive is next to the possessee? Or because the speaker is speaking hurriedly? ;)
I think you use the "la mia" in when the object of possession comes after the possessive pronoun. It's the same in english. "La borsa è mia"=the bag is mine " Questa è la mia borsa"=this is my bag
From what I've read, there are many reasons why you would or wouldn't use il, la, nostri, etc. but it is optional if there isn't a noun after the possessive adjective, as in: la borsa è mia (no noun after mia, so no "la" needed), not la mia borsa (noun after mia, so the "la" is required).
The "la" can be used if you want to distinguish something or emphasize:
la borsa è mia = the bag is mine (describing the object)
la borsa è la mia = the bag is mine - out of many bags (describing possession/emphasis/distinction)
This can be shown by other adjectives as well:
la borsa è colorata = the bag is colorful
la borsa è la colorata = the bag is the colorful one
I think it is correct to use 'la mia', but as it is a listening exercise we are supposed to stick to the exact phrase
It is my understanding the objective is to report what is said regardless of possible alternatives to the expression. Still, I would agree that your phasing is also acceptable - but that isn't what she said.
La borsa è mia=the bag is mine ( pronome possessivo )
La mia borsa= my bag (aggettivo possessivo)
Argh in any other context they demand article before possessive pronouns >\
è la mia borsa = 'it's my bag'. The subject is 'it'.
la borsa è mia = 'the bag is mine'. The subject is 'the bag'.