Can you provide a citation for this, even one example, ever?
Any payments for rent or anything else which contribute to the property or relationship, are taken into consideration by a court when said relationship ends.
I've seen a few fingers burnt by scenario's similar to this. Initially I'd go for a modified option B.
Person A owns house and continues to pay the mortgage.
Person B pays her half of the bills, person A pays his half.
This way you are both equally contributing to the upkeep of person A's property, while person A continues to pay for and keep 100% equity of the property.
If after a time you feel like everything is going great and she is the 'one' etc, then by all means go for option A, but only after legal advice with a view to a contract/agreement on what happens after separation.