I think that is right, since the freezing points / boiling points are also influenced by pressure. So when it tries to expand and cannot expand due to an unbreakable container, the pressure increasing substantially, and the respective points also change.

I'm sure if you try to boil water to steam, and keep it in a container that cannot expand, it won't convert completely to steam, since pressure increases its boiling point. With the conversion to ice, I am not exactly sure (something similar happens possibly) just because it is a little atypical in terms of volumes and liquid / solid states. Also, too tired to look this up :)