If a reference type does not override Equals/GetHashCode, a Dictionary using the default comparator won't care about any of the key objects' fields or properties, and thus won't notice or care if they change. It's simplest to think of the default GetHashCode method as returning a number related to an "object ID", and the default Equals method as comparing "object id's". Indeed, in a system limited to two billion or fewer objects, GetHashCode could simply return an object ID, but for various reasons it might do other things as well.
If the only part of an object that is examined by Equals or GetHashCode is the object ID, then for purposes of those functions, all objects are immutable. Once an object is created, it will always have the same ID, and that ID will never be used for any other object until all traces of the former object ID have vanished from the universe.