Cole, it really depends on the Chafing Dish or Steam Table.  If one is heated using canned heat (Sterno) you most likely will find the water will boil because of the lack of control.   The Steam Tables used in commercial applications will typically keep the water at a minimum of 160, the health department requirement for hot foods in most jurisdictions.  Most of these types of heating elements have a thermostat to regulate temp, as opposed to the unregulated Chafing Dish.     In fact a quick check with the board of health advises a minimum of 135F will keep food safe.

Food borne illness is a serious problem and most reputable establishments err on the HOT side.   

A lot depends on the type of food being kept hot and for how long. Heat sensitive foods like dairy dishes, sauce hollandaise, for example, will hold better over simmering water so that the eggs don't scramble whereas something like fried chicken needs to be kept hot to stay crisp so the water under it might be near or at boiling and there might be heat lamps over it. Fish was probably kept over lower temperature water. It was always dramatic when an empty or near empty pan of food was pulled and replaced with a new one. I would try to get a quick glimpse and generally under the entrees, the water was boiling as I'm sure it was under the baked potatoes and most of the veggies.

There was a big food poisoning outbreak a few decades ago when strangled eggs were cooked in huge amounts for breakfast buffets. They were not stirring them sufficiently and in probably too deep a pot so that the eggs at the center were not reaching the proper temperature to cook them to a sufficient degree of doneness to kill bacteria. They made people sick. It was not the holding temperature that was too low, but insufficient cooking that was the culprit.  I think it was before Pasteurized eggs were marketed. If you went to a breakfast buffet and wanted eggs, it was safest to eat eggs from the egg station where individual servings were prepared. I don't know if commercial kitchens have to use Pasteurized eggs or not. I remember at the Waffle House, there was a deep cylindrical container of readied eggs with a ladle in it on the counter near the cooktop  and eggs were ladled into the skillet and prepared to order. The gross thing to me about egg preparation was the nauseating smell of the hot butter or margarine in which they were fried.

Tom, I was very connected to Waffle House and do not remember any of the stores having egg shell eggs, broken before being cooked.   The only containers used for storage were indeed stainless steel and for grits and chili...only.  No eggs were ever pre-broken and ladled into a skillet to be cooked.   Waffle House was VERY cautious about food safety and most especially eggs.

So much so, all eggs had a limit as to the time they were allowed to be non-refrigerated.

Never would a unit be allowed to break eggs and have them ladled into a skillet.    If you witnessed this occurrence, some manager is about to be in trouble.  Big trouble!

I have two silver chafing dishes I've begun using after years of them sitting on display.  They have the alcohol burners below them and gets quite hot.  Unfortunately they only have the glass insert dishes and an open bottom that exposes the glass dish directly to the heat from the flame.  Many things I put in them scorch on the bottom, even if the flame is very low.  These are quality Sheffield silver and were not cheap, so I wonder why they did not allow for a water bath below.  I have another chaffing dish that does have a lower container for water and it does heat much more evenly.

I once had a metal-covered asbestos flame tamer that I used with a gas stove in my first apt. up here. That would not be available now, of course.  I wonder if you could maybe cut the bottom of an aluminum foil disposable pie pan and put it between the glass dish and the flame or, if the glass dishes just hang in the frame with no support underneath them, could you maybe use a  layer of foil, folded to make it more narrow, to form a strap under the dish that would be held in place between the dish and the frame to temper the contact between the flame and the glass, cutting off any excess that extended beyond the dish and frame.

Do the burners use liquid alcohol? You could try using 71% isopropyl alcohol which does not burn as hot or you could take out the absorbent wick part of the burner and use food warmer candles which burn much cooler than alcohol.

I've only been using the dishes for the last few years for large gatherings and bought a bottle of alcohol.  My thought was to find a dish that would fit into the heavy glass dishes and use a bit of water to moderate the heat.