Is the DataMember IsRequired attribute in combination with a Nullable type contradictory?

It can make sense if you want to initialize it with null and let user to set a valid date. So before submitting it can validate user input.

Here is a similar contradictory that may answer your question.

Interaction with IsRequired

The DataMemberAttribute attribute has an IsRequired property (the default is false). The property indicates whether a given data member must be present in the serialized data when it is being deserialized. If IsRequired is set to true, (which indicates that a value must be present) and EmitDefaultValue is set to false (indicating that the value must not be present if it is set to its default value), default values for this data member cannot be serialized because the results would be contradictory. If such a data member is set to its default value (usually null or zero) and a serialization is attempted, a SerializationException is thrown.

A guess: you MUST have a node for 'LastModified' (=required) but the contents can be empty (=value is null).