Only true for the WTA/ATP events.
ITF events , like Davis Cup, Billie Jean King Cup, a bunch of other per country competition (former Hopman Cup, or now United Cup) and of course, the Olympics, both players have to represent the same country.
The ISU is actually much more flexible than some other countries with country hopping.
Your beef with the IOC and the Olympics in general is bugging me because it doesn't respect the athletes' will and wishes. If they want to participate because it's their dream and that requires switching partners or even countries, let it be so.
I like the Finns but they were not on a good trajectory. I tend to believe that what we see on the ice is just a small part of what is happening in training. Look at McIntosh and Zandron... they were horrible on the ice... way below their respective talent. It wasn't working out for them. Who knows why but it could something as simple that one of them didn't like the training environment or that off ice, they didn't get along or whatever.... Izzo Ferland were not working out either... and Izzo seems happier skating for a small fed with a much less talented skater than Thierry was.
I am writing all this because whenever there is a split, some people often get pink coloured glasses about the former partnership. It wasn't working out great other the fact that they were giving Finland a team, which is something that hadn't happened in a long time (don't remember if they ever had one since I follow the sport).
To me, this is a good split. I wish both skaters the best and I hope they will find a way to achieve their dreams, including the Olympics, if that's part of it