I think it's primarily, maybe only, when a CC is loaded lower than a terrain. Dragging a character onto a terrain works fine, I believe. So the other workaround is not to double-click to add your character if using a terrain, but use drag-&-drop instead.

I used dragging and the issue occurs. See my description of the steps to reproduce in the Feedback Tracker. Regardless, I think it needs to be fixed before v7 comes out.

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Odd. That worked for me last time I had a go at this. I also used the plain like you did Anamagic. Now I'm getting the same behavior as you in both cases. But I also was playing with "set as bounding box" for the terrain, and it would give 2 varying results. The plain seemed to lose its "terrain-ness" if bounding box was on. I tried a block instead, and the bottom surface is where foot contact happened. When the plain lost its "terrain-ness", the grid became the floor again. Of course it is quite unusual to have a 2D terrain. We usually just use the grid, or have a shape that also has depth. This affected characters already in the scene. Dragging a new character seemed to always place on the terrain.

I think someone else gets the credit for turning off foot-contact. My solution was to put the terrain below the grid.

Good news: the terrain issue was reproducible by RL and has been solved. There will be an iClone 6.52, it says in the comments.

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That's great news! Glad you shared the steps so they could repeat it and fix it. :).

Doing  a search for the term "physics assignment failure"
I got this thread: https://forum.reallusion.com/255622/Physics
The thread is a year old, has a solution been found to why this occurs or do I have to also send my files to customer support?

It seems that props with sub-props cannot have physics.

This should probably be added to this thread as well: several users have reported various kinds of timeline issues in 6.51. For those affected there is a Feedback Tracker entry (Issue 781): http://www.reallusion.com/FeedBackTracker/Issue/Timeline-acts-irrational.

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I've encountered an issue with the Direct Puppet tool, and before I report it in the Feedback Tracker, I'm posting this to see if it is a known issue that I haven't been able to find. When I link an Avatar to a moving prop (in this case, the pilot of a plane, linked to the moving plane) and then utilize the Direct Puppet tool to animate the Avatar (just some simple head movements), things work fine during the Preview. But when I complete the recording, the Avatar is suddenly displaced far from the prop. It seems as if the motion root of the Avatar is shifted radically. Is this something others have experienced? 

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My avatar disappeared from the timeline. iClone hung during one of my saves. When I restarted iClone did a recover (restore) and the avatar was back on the timeline. I saved as a new name then opened a previous version and the avatar was again missing from the timeline.I hope that helps with debugging the software. Even though iClone 7 is announced, please fix the bug in 6. I just brought the Neuron plugin and suit. I'd like to be able to use what I have so far.