If I gather correctly, boiling the full amount including mash, sparge and boil off, you need a 40 litre boiler to do a 22 litre brew. I don't doubt some recipes ask for more and I haven't researched the intricacies of BIAB quite yet.
However if you look at the question, what is the absolute minimum you need the boil, the answer would be the amount you mash with, including any sparging. The minimum you need to mash is 2-2.5 litres per kg of grain. So for a 4Kg grain bill you 'could' mash with 10 litres of water. If you then do only a 5 litre sparge you could boil the 15 litres of wort, top up with boiling water once it's boiling and unlikely to boil over.
If you keep topping it up during the boil to that 15 litre mark, then when done you would add 7 litres of water to the FV. Better to test gravity and calculate how much water your mash efficency allows to reach your OG, or add boiling water with DME mixed in to make the OG.
All this is "minimal" and not "optimal" of course. Hop bill would need varied and to avoid adding DME due to low efficency you may need to up the initial grain bill 10-20% or so and recalculate minimum boil volume.
EDIT: In short, you only need to boil the wort that has come through the grain. If you can make the wort very high gravity, then in theory you can water it down after the boil. DME does not need boiled.