Swept wing in the Flying-V is clever way to get a optimal thickness-to-chord while keeping the total surface area in check.
(If I understand correctly, what is required is that its angle of attack is lower than the one of the main wing, or equivalently (if the wings have the same shape) its wing loading.)
See section 6.1 here, for example:
http://www.av8n.com/how/htm/aoastab.html#sec-basic-stability
But as the source you provides say: "indeed most aircraft operate with negative tail lift most of the time."
In practice all commercial aircraft have the center of mass so much forward that require negative lift for stability. If you look at the cross section of the horizontal stabilizer, it's like wing upside down.
See also:
https://aviation.stackexchange.com/questions/34963/is-a380s-...
https://aviation.stackexchange.com/questions/30400/will-opti...
Aerodynamically the wetted area that generates drag without lift is undesirable. You need a wing generate lift, but everything else is there for something else like stability, handling, payload etc.
In conventional "tailplane" configuration the fuselage and tail are just providing drag and almost no lift (tail has little wings 'upside down' generating negative lift and trim drag). If you have canard or some more exotic wing configuration you can have all wings generating lift but there is still drag from the body. In clean flying wing, there is nothing else except the lift producing wing.