Rookie Mistake

 Let us pause to consider the chafing dish itself.

There's a scaffolding that holds a water pan over a heat source and the blazer pan over the water pan.  The heat reaching the food is a very even 212° F, perfect for melting cheese, making delicate sauces, or keeping food warm at the buffet.

But the very name blazer pan seems to suggest it might be used a bit more aggressively.  And so it can.  You remove the water pan and use the blazer pan directly over the heat source like a skillet. This is how you can use the chafing dish for cooking performances wherein meat is browned and a fond created for rich sauces. This is how you create sizzle!

In retrospect, it seems obvious that for Steak Diane, you would want to use direct heat.  

 Illustration by H.W. Doremus from The Chafing Dish Cookbook by John and Marie Roberson.