"does the statement" is correct and usable in written English.
You can use it to introduce a question. For example, "Does the statement 'all dogs are mammals' mean that all mammals are dogs?".
What does the statement really mean?
Does the statement adequately address those concerns?
Does the statement "We hon it snowed with big flakes". imply "We hon it snowed".?
How does the statement made by Mary's doctor support Dr. Markel's assertion?
Does the statement "The 80's are back!" chill your blood?
"As in all our investments, Paulson has access to the same information that everyone else in the securities markets does," the statement said.
"I congratulate the Angels and their manager on the great job they've done," the statement said.
"Every detail of the work was scrutinized, criticized and finally approved before it could be done," the statement said.
"If there are health conditions that warrant another admission to hospital in future, this will be done," the statement said.
