They have been pushing this position for some time, citing 36 CFR 327.4, but it's clearly an incorrect interpretation.
36 CFR § 327.4 Aircraft
(a) This section pertains to all aircraft including, but not limited to, airplanes, seaplanes, helicopters, ultra-light aircraft, motorized hang gliders, hot air balloons, any non-powered flight devices or any other such equipment.
(b) The operation of aircraft on project lands at locations other than those designated by the District Commander is prohibited. This provision shall not be applicable to aircraft engaged on official business of Federal, state or local governments or law enforcement agencies, aircraft used in emergency rescue in accordance with the directions of the District Commander or aircraft forced to land due to circumstances beyond the control of the operator.
(c) No person shall operate any aircraft while on or above project waters or project lands in a careless, negligent or reckless manner so as to endanger any person, property or environmental feature.
(d) Nothing in this section bestows authority to deviate from rules and regulations or prescribed standards of the appropriate State Aeronautical Agency, or the Federal Aviation Administration, including, but not limited to, regulations and standards concerning pilot certifications or ratings, and airspace requirements.
(e) Except in extreme emergencies threatening human life or serious property loss, the air delivery or retrieval of any person, material or equipment by parachute, balloon, helicopter or other means onto or from project lands or waters without written permission of the District Commander is prohibited.
(f) In addition to the provisions in paragraphs (a) through (e) of this section, seaplanes are subject to the following restrictions: ...
(b) clearly prohibits the operation of aircraft (takeoff and landing) except at locations designated by the DC.
(c) prohibits reckless flight over USACE land or waters.
(d) acknowledges FAA authority over airspace.
So yes - they can prohibit sUAS operation from USACE land, but they have no authority to prohibit overflights.