That anything that uses electricity instantly melts and is forever unusable from that point on?No one is making such a ridiculous statement.
There are two major problems caused by EMP.
One is modern digital electronics, which are very sensitive to static electricity. If you've every installed memory chips in a computer, you were probably warned by the vendor to take precautions to avoid generating any static electricity. A shock too small for a person to even notice can and will destroy digital electronics. Note that many chips have special circuitry to protect against shocks being applied to the pins of the chip. However, an EMP would generate "sparks" inside the chip itself. This wasn't a problem prior to microelectronics, since old-fashioned vacuum tubes are practically immune to the problem.
The other problem is very long conductors, such as power lines, and cable TV and phone lines. The induced voltage and current from an EMP is proportional to the length of the conductor. Since these lines can be miles long, a huge spike would be generated on the lines, enough so that even devices without sensitive electronics could be damaged or destroyed.