Interesting you should say about adjusting the "set-back" temp, it's not quite clear from the manual exactly what this does.
The system works with two temperatures: Comfort (e.g 21C) and Economy/Setback (15C). The Comfort temperature is used during the day and the Economy during the night or when the house is unoccupied. The time/temperature settings determine when you change from Comfort to Economy. So at 6am, say, it will change to Comfort and at 11pm, say, it will change to Economy. The heating never goes off, in the traditional sense.
Normally the VRC400 is set to Auto, so it switches between Comfort and Eco at the appropriate time. If you change the mode to Set-back, it will maintain the Eco temperature all the time. Provided the Eco temperature is low enough, the boiler will not come on.
You say that the boiler is coming on when the inside temperature is 15C and the outside is 6C. 15C is the default Eco setting, so the boiler could be running to maintain that temperature, or it could be trying to bring the house up to the Comfort temperature - depends on the time of day.
As you don't seem to mind if the temperature is only 15C, you should change the Eco/Setback temperature to say 5 or 10C and the mode to Setback. This will effectively turn the heating off all the time, unless the temperature drops below the Setback temperature.
Also, the boiler was still showing a winter setting (d23) when the outside temp was 29C and the inside about 25?
Vaillant don't explain what this setting is for. Have you tried changing it?
Have you checked that the VRC400 has Room Temperature modulation set to 1?