Usually, the aquastat has a sensor that is in the boiler water, not the domestic hot water coil. The aquastat would be there whether you had a tankless hot water coil or not. The domestic hot water comes from a separate copper coil heat exchanger that's set inside the boiler, totally immersed in boiler hot water. Since it's a heat exchanger and not a tank like an electric hot water heater, it's called "tankless" hot water.
There are two ways the burner for the boiler will ignite. First, the water in the boiler drops below the aquastat setting. Second, when you call for heat at the thermostat. Again, the aquastat has not direct relationship to the domestic hot water coming from the separate coil inside the boiler. If you check the domestic water connections at the boiler you should see a temper valve. That simply mixes cold water with the much hotter water coming from the coil in the boiler. Now the gallons per minute for the tankless hot water will be dependent on the boiler water temperature... the aquastat setting. The hotter the boiler water (higher aquastat setting) the more allons per minute of domestic hot water you'll have.
The aquastat is set based on the heating demands of the house. For a steam system, the setting may be 160 to 180 since no heat will be forthcoming until the boiler gets to 212. For a baseboard system, the aquastat may be set at 140.
Now the lower you can have the aquastat set and still have comfortable heat, the less burner run time you'll have and that should make for lower energy use.
Can you tell us the other opinions you have heard and what logic they are based *