How does reflowing solder not damage the chip?

Reflowing is generally a short term heating not much longer than a minute maximum in production settings, and reflowing is hotter to melt the solder.

Overheating is a longer term proposition which causes damage to other components as well, that been said if heat applied during reflow is extended it will cause damage just as overheating will.

Carefully application of heat during reflow should not damage chips, and if you follow to the time and temperature suggestions in the ps3 guide you will not damage the chips and successfully reflow the solder under the chips.