As far as I understand, Monero allows Alice to create a public key for Bob that only Bob knows, on the fly, by using the following mechanism:
Bob's address: A = aG, B = bG, where only Bob knows a and b.
Alice's creation: R = rG, P = h(rA)G + B
This allows Bob to know that the private key of P is equal to h(aR) + b.
My question is, is this key creation process enforced?
For example, could Alice send money to a different P that is in no way associated with an address A and B, and is instead an arbitrary P = xG and simply generating a random unassociated R? Or is there a mechanism that I am not aware of that somehow prevents this?
My suspicion is that this is a valid maneuver, as it doesn't violate any of the unlinkability protections and is, as far as I know, undetectable.
EDIT: Just to be clear, this P = xG has not been used before.
EDIT 2: I should clarify that x can be a value known by Bob.