Front tire & downtube clearance - extremely dangerous?
Yes, extremely dangerous, as evidenced by your falling over the handlebars
It's evident from the photograph you linked, that the fork is pushed backwards, bringing the wheel much too close to the frame. The most likely reason for this would be crash damage, given that the fork is facing the right way.
There are two hazards then, one is locking the front wheel instantly under braking, while the other is hidden (or even visible) damage to the fork, risking structural failure. This is likely repairable with a new fork and inspection of the frame, but happily you've passed on purchasing this time. Caveat emptor I suppose