I was curious and looked it up, and well, seems like you are correct, but also it's all a bit of a mess and the MGB is part of a trio of companies of which one is the infrastructure (owned entirely by government), one is the management (owned half by the government, half by BVZ Holding), and one is MGB itself (presumably the actual trains etc.? Not sure) which is mostly owned by BVZ Holding.
So... yeah, we got some complicated company structures there too.
In real terms, yeah, considering a normal, non-business-management human being will see management and infrastructure as part of the Matterhorn-Gotthard-Bahn and those aren't 100% private.
I was curious and looked it up, and well, seems like you are correct, but also it's all a bit of a mess and the MGB is part of a trio of companies of which one is the infrastructure (owned entirely by government), one is the management (owned half by the government, half by BVZ Holding), and one is MGB itself (presumably the actual trains etc.? Not sure) which is mostly owned by BVZ Holding.
So... yeah, we got some complicated company structures there too.