Its interesting how the Wiki article talks about having the center of gravity of bike + rider shift to the left or right of the wheels to make the bike turn. This can be accomplished by leaning the bike or shifting the riders weight. It’s the offset center of gravity and not the lean than makes the bike turn.
When I first learned to ride, my MSF instructor focused on the need to lean the bike to make turns, and that to make the bike turn more you need to lean more. The bad thing about this is that I learned to lean the bike even to the extent of shifting my weight in the opposite direction in order to lean more! Its especially important on a big touring bike with not much lean clearance to make sure that you are not pushing the bike over too far. In tight turns, you need to shift your body weight so you can keep the bike as upright as possible.
When I watch Harley riders ride the canyons around here, I notice that a lot of them ride in a dangerous way – butt firmly in the seat, pushing their bikes over with the handlebars until the pipes are scraping.