This accident was a full-meal-deal of confusion on everyone’s part.
To start with, the static ports were still taped over from an earlier paint job. These ports are necessary for the instrumentation onboard - without a static port the airplane can’t reliably determine airspeed or altitude. (The whys behind this aren’t important here - if someone wants to know more there are plenty of people on this board who can explain it!)
So the crew takes off into the Peruvian night and immediately turns out over the water (Lima has those nasty Andes mountains to the east). At night overwater with little or no moon means almost no outside visual references.
As they climb higher the taped-over static ports become more of a problem. Basically their airspeed indicators started varying with their altitude - the higher they climbed, the faster the airspeed indicators read. What really introduced confusion was that all the airpseed indicators were reading the same - usually a “bad” A/S indicator will read differently than the others, thus identifiying it as the bad one. These guys had all indications telling them that they were going too fast as they climbed. In fact they got the overspeed warning horn - a loud, annoying clacker that tells you to slow down. So the pilot reduces power and brings up the nose - proper things to do in case of an overspeed.
Except that they weren’t going too fast - they were close to being way too slow. As they pulled the nose farther up the airspeed decreased more, and the Angle of Attack (AoA) increased to the point where the stall-warning (stick-shaker) actuated. Now these poor guys have two warnings in the cockpit - one telling them they are going too fast, and another telling them they are going too slow.
At night, overwater with conflicting loud alarms in the cockpit: a recipe for confusion. In desperation the pilots asked ATC what altitude and airspeed he showed them at. As others have pointed out, ATC radar cannot determine this on its own. It needs data sent to it from the airplane’s transponder. In this case the airplane’s transponder was working fine and sending data - the same BAD data that was being displayed in the cockpit. So the controller reads his display and tells the pilots they are doing exactly what their instruments say they are. The panic and noise in the cockpit were surely heard by the ATC guy, making him wonder what was going on. With unreliable data being sent to him, though, he couldn’t help a whole lot.
Eventually we all know what happened - the pilots continued to slow the airplane until it stalled, and they spun into the ocean.
With the luxury of hindsight and sitting in a well-lit room, we can find ways to prevent this from happening again. Obviously not taking off with the static ports taped over is first, but what about airborne with the problem? If the guys were head’s up enough they could have looked at their FMS for a groundspeed readout - systems based on inertial nav or GPS can give you reliable groundspeed indication without relying on other aircraft instruments.
But what really would have saved these guys was basic pitch-and-power settings. The old “does this make sense?” test. Does 20 degrees nose high and idle power seem like something that could overspeed a 757? Not to me either.
This accident has been studied exhaustively, and basic pitch and power settings are part of training in airline courses (with renewed emphasis).
Sorry for the long post - I got on a roll!