From the flight manual (1967 edition) we learn that
A glide from 70,000 feet to sea level will take about 73 minutes and from 35.000 feet to sea level will take about 48 minutes.
and, in section III (emergency procedures):
If it becomes necessary to reach lower altitudes in the minimum time, the descent can be made faster by remaining in a banked spiral and increasing the speed to maximum allowable IAS limits. The bank angle and stick forces should be varied as necessary
to avoid exceedig G limits and to stay out of heavy high speed buffet. The only disadvantage is an increase in general roughness. Shutting the engine down will increase the rate of descent but may result in windshield and canopy frosting.
Section VI warns that
The descent in the high altiude area from 75,000 feet down to 70,000 feet is slow. The engine power, even on minimum flow, is still considerable at this altitude and the drag items do not produce much drag at indicated airspeeds at 90 to 100 knots.
Now I wonder which exact type of U-2 your friend has experience in since those points in the flight manual all contradict his statement.
If even the landing gear should be lowered in order to add some drag, it is obvious that the U-2 needs all the help it can get to descend quickly. There is a hydraulic accumulator and a battery of 35 Ah, so even a power loss will still allow to deflect the drag items. However, without sustained hydraulic pressure, the speed brakes will be slowly pushed in by the airstream, so a power-off descent, while subtracting the still considerable idle thrust, will also cut speedbrake drag.
Again section VI:
The airplane has conventional speed brakes which are moderately effective. Their primary use is as a drag producing device for descent, approach and landing. […] The speed brakes are fully variable and can be set at any desired position. In some cases they will creep closed from an intemediate position after a period of time. They cannot creep closed from the fully extended position if the switch is left in the extended position.
The only reason for a slower descent with power off is the closing of the speed brakes from loss of hydraulic pressure. This will become more effective at lower altitudes when Mach limits allow to fly at an IAS of 220 knots (gust control to faired) rsp. 240 knots (gust control to gust). Still, the manual advises to shut the engine down in order to increase the sink rate. Windmilling should still create some hydraulic pressure, but the manual does not go into details here.