We have liquid fuel that goes thru tubes & lines.
We have vapor that goes to the canister and evap purge valve
We have VENT tubes/hoses that carry vapor and air (not liquid).
Just as your homes drain pipes have VENT pipes...the vent pipes allows air to escape up and out of your home, while the drain pipes carries away waste water to your sewer lines or septic system. The VENT pipes are only for air to escape...the same type of set-up is used in our cars. There are hoses/lines/pipes that are either for air, vapor, or liquid.
When dealing with a closed system like our fuel tanks and injection lines...we must consider that filling the tanks will require some type of venting...there must be some type of overflow drain tubes that will carry excess fuel as well as allowing air pressure to escape. And our cars also have a system of recovering unburnt fuel which is mostly in the form of vapor...the canister collects this fuel vapor, and the evap purge valve expels this vapor into the exhaust manifold to be burnt instead of wasting it away to the atmosphere.
FUEL TANK (exert from familycardotcom)
Most automobiles have a single tank located in the rear of the vehicle. Fuel tanks today have internal baffles to prevent the fuel from sloshing back and forth. All tanks have a fuel filler pipe, a fuel outlet line to the engine and a vent system. All fuel tanks must be vented. Before 1970, fuel tanks were vented to the atmosphere, emitting hydrocarbon emissions. Since 1970 all tanks are vented through a charcoal canister, into the engine to be burned before being released to the atmosphere. This is called evaporative emission control and will be discussed further in the emission control section.
If the fuel supply system is not clear as how it functions...then reading up on the topic using the online BMW TIS and finding the PDFs on e38.org & e38.org/e39 will go a long way in grasping knowledge...even googling the topic...may prove to be very illuminating.
You can see in this TIS doc, that there is a VENT hose (air). The 2 holes seen when refueling...are probably 99% assuredly spillage/drain holes that allow excess fuel that leaks from refueling or fuel that may get spit back up while refueling to drain back down into the fuel filler neck...and back down into the tank:
http://tis.spaghetticoder.org/s/view.pl?1/01/37/30
We must also remember that there IS a hose that sticks out from that side of the vehicle that is
#12 (the battery vent tube)...again "VENT" tubes carry air/gaseous vapors. I don't have the sedan...so are you 100% sure that the tip of the hose encircled in red is NOT the battery vent tube (#12 in the diagram)?: