This claim is false.

Law enforcement has the ability to get stored communications from companies like Twitter under 18 USC 2703(d). This is a famous "d-order" that has to be signed by a judge.

Companies can demand reimbursement under 2706. You can argue that 2703 should have a higher standard, but if the government can get to user data should it be free or should the companies ask for a nominal cost?

This is absolutely nothing to do with content moderation.