The flame on the hob and the flame in the combustion chamber will be the same temperature. The flame in the boiler will be about ten times bigger. Like the hob, the boiler will also produce invisible water vapour. It is only when it is deliberately cooled down later that it condenses back into water.
If you go back to the equation:
CH4 + 2O2 → CO2 + 2H2O
The molecular weight of methane is 16, and the molecular weight of water is 18. So, every 16g of methane we burn, produces 36g of water.
If a typical boiler is about 90% efficient, and burns at a rate which produces say 10KWh of heat per hour (in cold weather), it will burn about 11KWh worth of gas in that hour. 11KWh worth of gas is about 1 cubic metre of gas. The density of natural gas in about 0.7 Kg per cubic metre. So in that hour we are burning about 0.7Kg, or 700g of gas.
700/16x36 = 1575g
This means that the 700g of gas burnt in an hour would produce about 1.6Kg of water, which is 1.6L of water. So, the 2L figure sounds about right.