Can't explain the business about the magazine's effect on extraction, but if your barrel is a aftermarket replacement with a tight "match" or Bentz chamber, I have read about, not experienced, the issue you decribe. The 10/22 I had was stock and shucked everything, but my CZ 453, a bolt action, had a tight chamber that required a little extra effort to chamber some ammo, notably CCI Velociters and some others with wide driving bands or lots of lube. Kinda comes with the advantage of tight chambers. You might want to experiment with different brands of ammo to see if it fixes things. Then again, ammo that wedges into the lands a bit may shoot better, in which case you may want to live with it and unload with the trigger.
Anyway, I'm not sure what you're trying to accomplish in the situation you describe. Why are you loading a round, removing the magazine and then trying to extract the live one? If you're just unloading with part of the mag still loaded, extract the round, hold the bolt back and drop the mag.
Only in West Virginia would somebody avoid a proper clearing procedure.
Dave
