As the platform tutorial says you shouldn't have the behavior on an animated object, make sure you are using a non-animated box with the platform movement otherwise animations will intefere with the collision detection of the platform behavior.
If you don't want small falls to block jumps, just allow a jump as long as you've been touching the ground within the past, say, 50ms. You will probably have to set the vector Y manually since the behavior won't let you jump if you're in mid-air.
I don't know why you're asking about forcing a platform animation since the behavior doesn't actually set animations, it just fires triggers as guides which you can ignore if you like and replace with other events if it suits you better.