To start with, princess has a hypothesis not a theory. This hypothesis takes as a basis the existence of soul, which somewhat allows to explain magic logically. But what can be called a soul? As i understand it, the magic power could be felt by the multitude of people and cause some phenomena, therefore it exists. If it exists, it has to have a source. And that what can be called a soul, an innate source of human magic power.
With that magic power humans are able to connect and influence spirits, attracted to said power. Through spirits as mediums humans are able to cause phenomena, the nature of which are decided by spirit attribute.
Now we consider magic power a product of soul, but what is the nature of this very soul? Solving this problem calls for another question: Why is magic almost limited to nobles? It means that there are some factors connected with being born a noble that allow the usage of magic. If nobility is able to use magic from the very moment they are born, it most likely means that this factor or factors are hereditary. If not, these factors need further identifying, but we can exclude things that vary from noble to noble, and consider only the common. So as this ability is most likely passed down, we can assume ( if there were no previous cases ) that princess is unique to aristocracy. The only distinct trait of Anise, apart from her inability to use magic, is her memories of the last life, and from that we can make a connection between the two. We can't be sure what sort of connection it is, but apparently soul is related to person's past experiences and therefore personality. Unfortunately, we have too little information available, so we can't have a definite answer. But seeing as person can affect magic power by the use of chants and will, we can theorize that soul is indeed strongly linked with mind. According to this hypothesis, princess not being able to use magic maybe due to her mind being affected by memories of the past life. If we consider others who are able to use magic from birth, it may be inferred that it is because of their mind being unaffected by factors, which come from having past memories. To conclude, we can't determine these factors yet, but hypothesis about soul and magic being closely tied with mind certainly can explain many points.