No.
The collection belongs to the Canadian Railroad Historical Association, which is a private not-for-profit body. It is extremely uncommon for an important railroad collection not to be State-owned. Usually, when it is not State-owned, it is owned by the State body responsible for railways. In France, for example, the collection is owned by the SNCF and administered by a not-for-profit body.
In other countries, the collection is under State ownership. In some cases, it is owned by the Department of Transport or the National Railroad Company, but in general collections are State-owned.