Sea legs first: My take on this was always that sea legs referred more to the ability to walk steadily while on a rolling ship than on the inability to walk on steady land. My own experience in this matter was as follows:

My first time on the ship, a large and somewhat top heavy cruiser which rolled quite a bit in relatively calm seas, I had no problems walking steadily. When I first hit dry land after that first voyage I was a little wobbly. Subsequent transitions were totally uneventful.

I, too, had never heard that taking on water was necessary for listing. Sufficient, yes, necessary, no. Unbalanced cargo could cause the same condition.