Well if it's doing it without the engine running then it seems unlikely to be a fuel pump problem - and as you say, it shouldn't have one fitted.
If it's like all my previous bikes (MZ excepted) then I'm pretty sure that the "breather" pipe is NOT actually a breather pipe. The tank usually breathes thru' a tiny hole in the filler cap.
Instead, the pipe should be merely an "over-flow" drain pipe - any fuel spillage (or rain water) collecting in the step-down area around the filler neck should dissappear down a small hole. This small hole is connected via a pipe INSIDE the tank, to where it exits at the rear, underneath the tank, for the connection to the rubber hose which dumps the spillage over your rear tyre.
So, I think that you *should* be able to blow up the rubber hose, and the air come out thru this hole near the filler neck, regardless of whether the filler cap is open or closed. The fact that you can't suggests there's a blockage / damage to the internal metal pipe.
Even if the tank is pressurising (which seems likely since the problem stops with the cap open), this shouldn't be able to force fuel out that's BELOW the level of the filler cap screws - it would simply force air out instead. If the fuel was bubbling and foaming to a silly extent then I guess maybe it could - can you see the fuel? Is it foaming like a hot tub?
BUT, if the internal over-flow pipe was ruptured below the level of the fuel, then any pressure build up in the tank could then force fuel up the pipe until it came out in the area around the filler cap. Normally it would just allow fuel to drain out of the rubber hose all over your back tyre, but if the internal pipe is blocked then that couldn't happen.
I'd be inclined to unbolt the filler cap allen screws, and temporarily "cork" the filler neck (need to make a good seal). This way you should see where the fuel is actually coming from.
Still not sure how the tank would be pressurising. Possibly a chemical reaction to something in the tank?
arrrf.