I was going to check up on something after work, but heck! I would probably forget! 🙂
The walk behavior does not record the position in the timeline, just that it is walking or not. It relates to things like physics, as you can collide with physical objects and the character will stop moving forwards. So yeah, it keeps walking from where it was if you scrub the timeline.
One solution is to make the Walk behavior not update the X position of the character. I think it was Body Speed? Then you use key framing to move the body (you animate Position X). That way the scrubbing of the timeline works, but you have to get the timing right to avoid the character looking like they are skating.
My hesitation is I thought I remembered something about adding the ability to sync the position so scrubbing would work. Was it "Position-based" instead of "Left/Right arrow keys"? Like if you change the position it would walk the direction needed? Ah, I think that was it. Don't use Left/Right arrow keys, use Position. Then if it moves fast enough it walks. Then you can scrub the timeline.