I think it's important to get cause and effect in the right order here - you can't have a short squeeze with out price rallying first ie price rallying triggers margin calls on short positions. This then adds to pre-existing buying pressure.

Remember, people getting squeezed are, for arguments sake, "dumb money". Initial reversals are caused by "smart money":

• Short-sellers taking profits (margin only).
• Buyers opening new positions (margin and spot).

The dumb/smart classification is of course an over simplification as some of the people getting squeezed are being trailed rather than liquidated etc.

Regardless, the "dumb" traders are on the wrong side of the market and the "smart" traders are correct. The smart traders cause the rally, the dumb traders are affected by it (and then affect it indirectly, reinforcing existing momentum as their positions are liquidated/covered).