How does the metal of a baking sheet get burned?

A natural gas flame is about 1950 C or 3540 F, so yes, a lot hotter than 500 degrees. (source)

Electric stoves will get red hot, indicating a temperature in the range of about 500-900 C or 770-1220 F. (source)

I take it this is an Induction cooktop/electric glass cooktop.

"Induction cooking is performed using direct induction heating of cooking vessels, rather than relying on indirect radiation, convection, or thermal conduction. Induction cooking allows high power and very rapid increases in temperature to be achieved, and changes in heat settings are instantaneous" - Wikipedia, Link

An electric glass cooktop uses electricity to first heat a burner. The heated burner then heats the cookware in contact with it - baconappliance.com, LINK

Because it is directly heating the cooking vessel, this induction stove will "cook" your metal directly, not boiling what is inside of it. It's the same principle as all kinds of stoves basically, it cooks your pot.

So, without anything inside of it the heat will be rise quickly (and because it's thin nothing like a pot), it could reach up to 260C (500F)Link. But this is depending on your stove because some stove doesn't have thermocouple to check the temperature it only adjusting the power of your induction, and it will rise quickly to 300C or who knows in max setting on the knob..

The black burns will show up because it reaches the temperature to burn the outer layer of steel because lacks cooling/food inside to cook it.

Edit:

"How hot does a stovetop get on high? I have found that using an IR thermometer to read pan bottom temperature after 5 minutes of heating (the temperature is no longer rising), that high corresponds to 375 degrees F, medium-high to 330 degrees, medium to 300 degrees, and low to about 275 degrees." - expandusceramics.com

so either you have the induction cooker that has more capability to reaching more temp, or you have an electric stovetop that has a broken thermocouple or it sets to max temp.

edited to correcting my dumb :)