a bitcoin ASIC can mine any coin that is SHA256
How would one go about using the Bitcoin ASIC to mine the alt coin also based on SHA256?
You have to use pool which allow mining alt coins
Not true, I have been solo mining Zetacoin with my erupters. -o 127.0.0.1:port
You can mine them, meaning that cgminer will allow you to try to use the wrong hashing algorithm to mine the coins, but it is impossible for something hashing SHA256 to successfully solve a block on a network with a different hashrate. CGminer will display your hashrate and everything, but you will never find a block.