I'm interested in how this person did anything to you-- as in, did the limpness go away and get replaced with regular old arm- and shoulder-driven movement when they were nage?
...stuff their arms into their bodies and then use their arms to throw their bodies. There's no point in letting their lack of understanding be reinforced. Keep throwing them till they get that, that type of "relaxed" is nonsense.
Some more thoughts on the memory...
I tend to be a softy (a tight-shouldered softy), particularly when I get the sense the other person isn't a very "physical" person and, more to the point, is uncomfortable with physical force. I would still try to control the trunk through that "noodly" arm though. It was tricky establishing any feeling like I had any connection to it. She certainly made me feel strong, which doesn't happen very often. I remember she reached a point where I had a much easier time feeling the intent of her actions (she became "denser" on some level of action). I remember I kept thinking about the "rule of 10." So at first I would guess I had to use a 9.5 to her .5 input, but over time maybe it became an 8 or 9 to 2 or 1.
One thing I just remembered in working with people I felt "stronger" than, and which seemed to help in general, was to look for the "edge" of their ability. As nage I would try to make it so my newer ukes were just about to fall over and then let them (even tell them to) "fill back in" through the connection point, at certain points in the movement. As uke, I would generally try to push that edge (if I could aproach it at all), though very gradually. Another "trick" would be to tell them to hit me with their free hand (trained folks already tend to do this) since this seemed to at least engage more of their body into the movement. For my very low level of operation, i was generally just happy as long as I could feel an incoming intent.
I do remember being very surprised one time when I was uke and the woman I'm thinking of controlled me in a much more definately way (not that I've ever been a measure of powerful). She had been getting a lot more direct hands-on with sensei and worked hard on having better "coalescence of power."