My experience has been moreso along the lines indicated by Cady and Michael.
Let's say that the "state of nothingness" is what we refer to as Mushin (No Mind). It is often accompanied with Mu Gamae (No Posture) when speaking in Budo terms. In the physical, technical sense these basically mean that in dealing with conflict our minds are not fettered or distracted by a multitude of thoughts or our bodies are not set in stances or postures that make it difficult for free movement in all possible directions.
Regarding the original post, I am relating the concept of nothingness/oneness directly to the act of dealing with conflict and the use of timing in accordance with physical Aikido principles. The comment that I quoted indicated that when one achieves this state of oneness or nothingness the concept of time is unimportant. This by its nature renders the concept of timing also unimportant.
This makes some sense if we see ourselves as directly connected to the source of the conflict for the sake of redirecting its energy along a non-destructive path. In this light the source of conflict and the source of resolution are in fact different elements of the same reality, thus a connectivity or oneness is achieved between Uke and Tori in an Aikido context.
The question then is how do you develop this in your own training, or as an instructor how do you foster this in your students from the earliest stages? For most practitioners (including Yudansha) the changes in the speed of an attack will have a direct effect on how timing is used to deal with that attack. The speed directly affects when
you decide to get off line and often how
you decide to do so. The modifications in timing to deal with different speeds of attack may be negligible but if they are miscalculated the result is a failed technique since initial avoidance of the attack will not be achieved or Tori moves too early, inviting a change in direction of the initial attack or a follow up attack to Tori's new position.
Getting back to Cady's example I have found that this ability to instantly deal with whatever attack is coming towards Tori is most times found when Tori is under severe pressure with attacks in rapid succession. In this case there is no time for the mind to settle and become attached to anything otherwise the attack lands, the body also adapts accordingly, not being given the opportunity to set itself into any static posture due to the high likelihood of being struck.
From my experience, training that is done too slowly allows the mind to wander a bit while the body is engaged in the activity of excuting waza. This wandering can easily entice the mind to become fettered on something other than the situation at hand, resulting in a loss of connectivity with the Uke and the potential of being surprised or taken off balance. The act of surprise itself is directly related to the disruption in mindset and posture.
In our training the "nothingness" state is developed by using drills and randori practice to get the beginner out of the "reactive" mindest into a more proactive mindset. One does not "sit back" mentally and physically to wait for Uke's attack and then respond but one is encouraged to connect with one's partner is such a way that every miniscule movement of the mind/body is detected, allowing Tori to instantaneously detect suki in the attack and enter. Over time this developoment becomes less and less conscious and becomes more ingrained as a natural movement in response to the attack. If the speed suddenly changes one instantly detects the forces that pre-empt the change and adapt accordingly.
Anyway that is what I was thinking when I heard the original quote and asked the original question. For beginners it is important to achieve a good feel for timing before one considers transcending timing via mushin. But that is imho.