I dont think your definition and mine are the same. I didn't mention grabbing 'lightly', not sure where that comes from, a forum is a bit like chinese whispers, things get distorted along the way. I mentioned 'relaxed', with full intent, free to move etc.
I have no problem with people practicing with whatever level of grip that they like, if aikido is valid it has to work with all levels of strength and types of attack.
What I am certainly not advocating is some limp/relaxed hold that has no intention, that would be a complete waste of everyones time.
The hold itself is only one aspect of the whole person. If uke holds with a relaxed grip (and I realise it is the word relaxed that is causing the problem for some), but with their mind on the target, basic standing or dynamic movement, makes no difference. Then they are in a position to follow nage's movement with ease. If uke's structure/co-ordination is correct throughout, then any use of 'muscling' a technique, runs into a big problem, as it is very difficult to throw a whole person with something as ineffective as tense arms.
When I am teaching, I constantly use this method to find the point at which the student is 'going wrong'. This method relies on co-ordination and a non-fighting mind. Uke's job is to follow the truth in the movement, to decide nothing and provide the intent for nage to work with.
I have been working with trying to understand and practice this as taught to me for quite a while. In the begining I was really into the training and what my teacher was doing, but I must admit, I was sceptical that it had any martial merit, it all seemed a bit 'soft'. It took me about 5 years before I began to see the logic behind it all. Now, I wouldn't want to go any other way, unless it could be proven to be more effective.
If I want to test myself against 'strength', my assistant teacher is a 'Dry Stone Waller' by trade, he lifts and places rocks, hammering and chiselling when required. He has a grip that can cut your circulation off
If I ask him for the sake of demonstration to 'apply a serious grip'' he knows what is coming next. For me the throw is easy, for him the fall is much harder than if he stayed relaxed and co-ordinated.
As for the 'centre in the hands' point. If your hands are not an extension of your one point/hara/centre/dantien, then you do not have the mind/body structure that is required to manifest the elusive aiki/IS that is much talked about. The hands must be connected to the ground, through the centre (not the centre of gravity/although it's in approximately the same place) This I realise, is the most problematic part of reaching higher levels of competence in aikido. If I am uke and am following someone's technique, if their hands are not an extension of their centre then they have 'lost'. Not that it's about winning and losing of course, just trying to constantly improve.
Not a full explanation, by any means, but maybe enough to gauge where you are on this continuum. I could just cop out and say 'it has to be felt', it does. Hopefully, this might clear up some of the tangents that this thread has gone off on.