I agree in sentiment however then the burden shifts to proving that person C was not really person A, and therein lies the crux
First: No. The burden is on B to prove that C is A, the default should be that if they cannot quite definitively identify the counter party then tough cookies. And they need to do this while covering all expenses and time value with interest in the event they're mistaken.
Second: if only! Most identity theft is not even remotely subtle. It's people walking in with mediocre quality forged documents or minimal info literally hundreds or thousands of miles from any location C has ever visited in their lives. Or someone randomly claiming to be C via some simple 10 digit government number and an email address C has never used. Etc etc. It's not exactly mission impossible hacking-a-passport-and-wearing-full-3D-facial-prosthetics-and-voice-changer stuff we're talking about here. Standard "ID theft" is just from a financial party with all the incentives to push through acceptance as frictionlessly as possible and then simply hound whomever they can try to pin it on and feed them into "debt collection" systems until most people cave.
What the law needs to recognize is that everything about this should be literally criminal. The original criminal is the one who committed the original fraud. But everyone who goes along with it from then on out, every single 3rd party directly trying to steal money or time or whatever from the innocent victim, is an accessory to that fraud. All of them are involved, though as always they can seek (after paying their penalty) to shift expense/liability back up the chain if they can prove it. It's their fault for insufficiently verifying the original counter party, and then they've compounded it by seeking to defraud someone unrelated.
Right now, in the interest of increasing commerce, we're forcing everyone in society to bear the burden of this specific fraud and the benefits go to the lenders. If person A is being defrauded by person B pretending to be person C, then person C has no reason to be involved unless they aided person B.
This is placing the burden on consumers in a different way.
The burden is lifted from the rest of us who somehow got tasked with making sure lenders aren’t making errors with the risk of losing hours of our lives fixing someone else’s problem.
It’s ridiculous that after your child is born, you’re supposed to spend your time to place a credit freeze at the 3 credit bureaus. Transfer the liability of identity fraud to the lenders, and they will figure out the solutions in no time.
This feels like an idea that would benefit consumers and be a business opportunity targeted at creditors if we could only convince them this is their responsibility.
Each party is verified and the relationship is verified to ensure non-repudiation.
An identity verification system would require the individual establishing their identity with the credit agency and provide as much or as little credit establishing information.
When a B2C transaction is established, the customer would provide the business with a token identifying the credit profile they want to use and the business would request a credit chect with it to the agency, and if the business accepts the credit score they can both acknowledge to the credit agency they wish to do business.
Party B thinks Party C owes them money.
Party C thinks they do not owe Party B money.
Party B sues Party C and shows (or not) by a preponderance of the evidence that Party C owes them money.
The onus is on Party B.