As I am not licensed to practice law in any canton I am careful how I phrase my answers. Suffice to say, the aide-memoire does not say one needs to change domicile within Switzerland; but I added the operative word "may" out of caution. and told the OP to ask the Land Registry.

I am well aware that both the Justice ministry and the various land registries may go beyond the law: I was myself convoked for a hearing on the basis that a flat that I bought "might" have been financed by my non-Swiss (but EU) national spouse. As it happened the Commission foncière decided the case in my favour on a surprising (and, I think totally irrelevant) basis: that I could have bought it with the proceeds of the succession of my Swiss-citizen mother. Whether or not it was my spouse's funds that actually paid for it (money being fungible, etc.)

The law, and AFAIK Confederation policy, does not, or should not, look beyond my own (Swiss) citizenship.