Well - when I hear the words "Space Heater" I instantly think heavily or over-loaded circuit.
Could there have been anything else on the circuit? Some of those things are 1200W, in the past I have seen some old plug-in models at 2000W. Chuck grannies old space heater on with a few lights and other detritus - you could be over the capacity of the circuit. Run that all winter long. Add one weak connection, that gets weaker every winter they supplementary heat the house with a high resistive load through the weakest link of the electrical system - I think the pictures spell it out.
We have been focused on the terminal connections vs. back-stab route here. IMO the appliance itself, and the often weak or worn connections inside the receptical are more likely the way to point blame.