Hard to be sure, because he was a pretty weird bloke :-)
But I don't think he meant that techniques should not be tested. A lot of aikidoka obsess over this "non-competition" stuff (aka "not fighting", which was another thread a while back), with the result that uke always cooperates, and they end up doing "happy dance" aikido.
If that makes the people doing it happy, then OK, but it is no longer a martial art, IMO. Going the other way, I also believe that turning a MA into a competitive sport (eg judo, karate, TKD) diminishes the art (and Ueshiba may have thought that too).
The only stuff of Ueshiba's I've read (always in translation, as what little Japanese I once had is long gone) that seems different from what other MA masters of the same period (Kano, Funakoshi, etc) had to say is this "budo is love" business.
I'm not quite sure how to take that, myself (although I suspect it would help to be a highly skilled, weird little Japanese bloke <g>).
I don't think it's the same thing as "not competing", though. All the old guys say the same stuff about not meeting force with force, hitting something hard with something soft, mushin/not focussing on winning, etc as well as character development. I think it's more likely Ueshiba meant (at least mostly) the same things.
 Karate people tend to forget this one :-)
 Aikido people tend to forget this works both ways. And also about the hitting part :-)
Well, from training in internal skills, which I call aiki, I find that once I start thinking about uke and the effect uke is trying to have upon me, I lose. In other words, once my mind starts defining me and my actions
in relation to another person, I have competition and I lose. Let me define that a bit more. When I say "competition", I do not mean it in the very strict sense of the word as used in Judo Competition, UFC Competition, etc. I'm defining it in a very ego centric sense in that it is related to me only.
Once my mind lets go of uke and uke's actions upon me, I find that things work. (In the limited sense that I'm not very skilled at aiki yet.) In push tests, the more I am focused on uke or uke's push, the less I am stable. That internal competition is a type of thinking that disrupts aiki. There must be no competition within me. And when I am fully vested in what I'm doing with aiki (internal skills), then uke disappears and there is only one body. I liken it to Ueshiba when he talks about being the bridge between heaven and earth. If my intent is strong upwards, then I can be the heavens over uke. If my intent is strong downwards, then I can be the earth under uke. I become the bridge between both and since uke now becomes a part of me, he/she then becomes the person/spirit traveling the bridge.
The bonus to all that is that I'm also not meeting force with force. I'm using aiki to split, redirect, store, ground, etc all the incoming force. On the opposite side, once I start thinking of uke and what uke is doing, I start to meet force with force.
Now, tactically, there is also a version of no competition that I think is being used. There is a thread at another board that someone posted some very useful information about this idea.
The idea is that you never receive on a straight angle.
You are receiving along points on the arc. No arc? Make one. Therefore there is always a tangential meeting where you can receive and feed along any point on that arc. You can even make it appear to be linear-eve though it isn't.
If you think of a straight line hitting an arc at any point it may help. The contact point becomes the pivot point or nuetral point. lets say it's the middle of the forearm. If the elbow moves negatively, then the wrist or hand moves positively proscribing the arc around the person.
In essence, you're creating no competition by using circles. You don't meet force with force. Sound familiar? In one way, it's very good tactical jujutsu skills when you move the body around physically. Add in aiki and you suddenly have a very strong, powerful skill set like Ueshiba had. All the while espousing no competition, never meet force on force, etc.