Wikipedia is often riddled with awful English. Many of the people who write or edit the English articles aren't native speakers, and I wouldn't necessarily believe someone over there who claimed to be one.
I'm not sure that's the problem with either of you in this case; you may be just saying different things. Yes, the chin must clear the bar each time, and that's a clear, concise, idiomatic way to say it. I would actually just say with each chin-up or pull-up; 'hoist upward' sounds rather awkward, but maybe that was already some other Wikiverschlimmbesserer, not this person.
However, to really do it right, isn't there also something you need to mention about the angle of the chin, or better perhaps, the jawline? If you think of the underside of the jaw as being a flat plane, that plane needs to remain parallel to the ground (and to the bar). That is, you can't wimp out by tilting your head back and pointing your chin up so that only the tip of the chin clears; you need to keep your head straight in normal upright position.
If you think of the underside of the chin then as being a line instead of a plane -- that is, drawing an imaginary line from the tip of the chin backward toward the neck -- then yes, it might be okay to say that that line should be perpendicular to the line of the bar. It seems to me that what that would really mean, though, is that you're not supposed to turn your head to one side or the other, not let your chin stop pointing toward the bar.
And I think you're right that people don't usually think of the chin as a line anyway, so that that description isn't very clear.
Not sure if this helps; maybe between the two of you you could come up with a new draft that takes the angle of the chin or jaw into account, but in a clearer way.