When falling from above, it is possible (though difficult) to directly grab onto the bottom side of monkey bars (discovered 2018-12-08 by Thermospore)

Dropping off

There are many instances of people randomly dropping off Monkey Bars

Many occurences seem to be in Crow, but this could simply be because there are many Monkey Bars in the level, not because they are especially cursed.

limbus theorizes it could be happening when crossing the seam between modules, similar to how you can get stumbles when running over seams. This needs more investigation, but seems plausible (discussion)