Measuring the length is a time-dependent process. To be clear, I am not saying that the rest length of the object changes as a function of time.
If you are moving relative to another frame it is not sufficient to place a meterstick next to the object. The way Einstein thought about it was to use a synchronized series of clocks along the length of the object. The measured time on clocks at the endpoints are then used to determine the length as the object
passes by. See the the first paragraph of
http://en.wikipedia.org/wiki/Length_contraction#Basis_in_relativity for more on this.
I think I should also clarify what I meant earlier. Say you measured a meterstick moving at some relative velocity to your frame. At this point you might say that the observed length must be contracted as a consequence of time dilation. This is where I don't agree with you. I don't consider time dilation, defined as "dimension of coordinate time changing due to a relative velocity," to be the fundamental cause of this effect. I consider relative velocity combined with a constant speed of light to be the cause. That is what gives rise to time dilation and length contraction simultaneously, not one after the other. This is a subtle distinction but I stand by it.
Edit: the point is if you apply the above reasoning to the original question of whether you can distinguish between time being slowed or the processing being slowed due to changed geometry, it means you can't.