I think your first post is mainly due to how the time of collision will vary according to the framerate. With a low framerate the objects can be overlapping a fair bit when a collision is triggered. With a high framerate the collision will be triggered closer to when the object just come into contact.
Framerate independence mainly just ensures the motion is consistent between collisions for any framerate.
Here's a test of different ways to do the integration for projectile motion, aka jumping. It also tests what they do at some different timesteps. The first method undershoots at lower fps, the second overshoots, the third is perfect at all fps, and the last is wrong.
I also compared it with the platform behavior, and it is using the perfect method when jumping off the ground, and actually is improved over how it was in C2.
The difference between jumping in the air, and jumping on the ground could have something to do with the logic to handle moving platforms but that's just a guess.
Actually looks like it's using method 3 when on the ground and method 4 when in the air.
dropbox.com/s/a5qzfvv7y18c3hy/plat_dt_test.capx