'if it can be proven that either at the time of purchase or at some later point in the party’s relationship, there existed a common intention between the parties that said parties would acquire an interest in the property.'
That will be difficult. The general tone of Melissa's actions indicate that she intended to scam her own parents, right up until the foreseeable end to the scam. There is no indication that she underwent any kind of reformative action to guarantee the ownership of the place in the hands of her parents, or brother. On the contrary, she actually created a will that left a property she never owned, and only rented as part of her registered Real Estate as an 'inheritance' for her brother. .
The parents may have been under the impression that all was tickety boo, but Melissa's actions indicate the exact opposite. This is where their claim comes undone, basically. They have to prove the claim that Melissa's intention as well as their own was genuine and legally correct.