What's The Difference Between A Power Surge And A Power Outage?

Did they check it for BROWN OUTS?  I would pursue that avenue...in lieu of a surge of energy it is a depletion of energy...good luck♥

What the rep says is not logical, "Power outage" means that there is no power in your sockets at home, and if there is no power, then how did all of your electronics got burned?

I think you should take the SP to a third party technician who is  certified on that kind of SP's, and get a second opinion

The difference between a power surge and a power outage is that a power surge is that the power goes out temporarily and a power outage is where the power goes completely out for hours.

The power surge is caused by things like a lighting strike hitting a power pole near you.  The extra electricity from the lighting strike can overload and burn out many things like electronic equipment, motors, lights.  If the strike causes damage to the power line, or overloads the power company's fuses at relay stations, it will cause a power outage.  
So the surge comes first, then the outage.
Before the power goes out, after a strike occurred, the voltage from the power company can drop from 115 Volts down to lets say 70 or 80 volts because of all the damaged devices connected to the power grid.  You will see the lights dim for a few seconds, them go out.  This low voltage can cause some equipment to fail.
It is also possible, that the lighting strike came in to your house from a phone line, a cable tv wire, or through a water pipe which could then jump to one of the others.  If this happened, the power surge protector can not protect against it.  It only protects that electric power connection.  
Oh and by the way, you could still have had a low or mild power surge, and depending on the rating of your devise, if may not stop the surge.