Yeah, Jamie pretty much nailed it. It's a question of load... the engine isn't under enough load in a free rev situation to spool the turbo decently because it's only working against internal friction. The waste gate will be closed or close to it when just free revving because the turbo isn't getting enough exhaust pressure to spool at any appreciable boost level. You'll also notice that to hold a 5500 rpm "idle" free revving takes very little throttle, hence, low load, hence, low exhaust output. That's where auto's are nice, you can brake torque and use the brakes as a load, with slippage being taken up in the torque convertor.
With a stutterbox you cut spark so you can run WOT at 5500rpm, additionally some stutter box setups will only cut spakr, not fuel, so the extra fuel will be at least partially combusting in the exhaust manifold and creating a larger than normal pressure differential across the turbine. Severely retarding the timing will also result in fuel combusting later than usual, meaning: in the exhaust manifold, that's how the anti-lag setups on WRC cars work AFAIK.