All modern high speed motorcycles produce downforce at speeds. Turbo charged Hayabusa's have reached over 225mph with stock body work (the only mod is usually a longer swingarm to reduce wheelie reaction). The main issue with a tunnel is that the air is trapped somewhat, increasing aerodyamic forces a bit, more drag and more downforce.
There are a lot of cars that produce upforce at speeds, making them dangerous at high speeds. Most cars are shaped too much like lifting bodies. This is why a lot of high powered European cars are speed limited to 155mph (250kmh). The first year production Audi TT had lift at the rear end, combined with a somewhat oversteery suspension setup, causing many of these to spin out when driven on the Autobahn, with some really bad accidents. They got functional rear spoilers and less oversteery suspension setups the next year.
Regarding the statement about driving a race car inverted, this would be possible in any car generating more downforce than the weight of the car. Forumla 1 cars do this, as well as the USA Champ cars, and probably the IRL cars. The speed that downforce equals weight is adjustable on these cars, usually around 115mph for most road courses, but at a much higher speed on high speed ovals (only IRL cars run these anymore). With Formula 1 cars, the downforce is produced by the upper part of the body and wings. With Champ cars and IRL cars, under-body tunnel effects also help to produce downforce. FIA doesn't allow this on Forumla cars, they get flat wooden skid plates instead. The Champ cars reduce pressure underneath them enough that when running on street courses, sewer tops are welded down to prevent the lower pressure from popping them out.
The wings of a plane produce lift by accelerating air downwards. When flying very close to the ground, you get ground effects, that would increase lift at the same angle of attack. Less angle of attack is used to maintain lift equal to the weight of the plane, with less drag. Same thing would happen if the plane were flown close to the roof of a rectangular tunnel.
Actually a good argument for wings producing downforce is a large closed box. Imagine a 50 lb box, with 50 lbs of air inside. The total weight is 100lbs. Air exerts it's weight on the interior of the box with pressure differential, more pressure at the bottom, less pressure at the top, with the net pressure differential just being enough to create a net 50lbs of downforce on the box. Using this example, remove 1 lb of air and insert a 1 lb flying model. As long as the model isn't accelerating vertically, it creates a pressure differential within the box, just enough to match it's 1lb weight and this closed system continues to weigh 100lbs.
Bernoulli's laws are just a way of describing the conservation of engergy, the total potential (pressure) and kinetic energy (note that kinetic energy is frame of reference sensitive) are constant if no work is being done. What's often ignored in the case of objects moving through a gas or fluid is that work is being done on the gas or fluid and the equations need to be adjusted take this into account.
A high speed bike going through a small tunnel will just get more downforce and more drag., but a car with lifting body properties might have issues going through a low tunnel at high speed. If the tunnel were also skinny, then drag force on the car would increase, as the car would be similar to a piston in an engine.
