It's a contradiction, yes.
I don't know if Aikido will ever find a way out of this contradiction. I doubt it, because its prerequiste would be having Federations acknowledge the contradiction.
But why should they? Why?
Besides, after all, we can see videos where O'Sensei trains aikidokas exactly in the way most dojos do.
You are alone with this Sphinx, Reuben. You have to find yourself what of Aikido is usable and what not. Nobody's gonna tell you.
Go find a partner off the mat, and check with him - then back to the dojo - then back to check out of the dojo whether what they told you holds "true" against fire
To date, I have found no better solution - and most of my techniques suck, in fact.
One wonders: do they know that a determined opponent grabbing your hand will NEVER let you place an ikkyo on him?
They make you spin ukes around with iriminage: one wonders, do they know a real attacker will NEVER let you bend his neck with a fairy tales touch?
They make you do ude kime nage against ukes whose consistency is that of leaves in the wind.
Go to the dojo. Then double check outside of it.
Find your Aikido - it won't look beautiful, probably - pretty aikido is for -ahem- demonstration purposes
If you are to be one day good at it, I doubt you will become such going to any Doe Dojo thrice a week. I really doubt it.
Aikido is an art of deception