Says who? Putin if I'm not mistaken. That is of course until Putin actually invaded. Before there was no real ask. Not to mention that you can only join NATO after an unanimous vote by its members. Just ask Sweden.
Sure it allows them to integrate the military of it's member states.
So let's play out Ukraine being a member state having a military supplied by America. (Not that you really need to be a member for that) Ukrainian combat readiness goes up.
So they can attack a nation 4 times their size armed with nuclear weapons?
Yup sounds logical. Again there is no treat from other NATO states in the event that Ukrainians are suicidal.
As to what the US position was. Again at best, and again NOT something that is supported by all historians it was unofficial. Russia OFFICIALLY declared they would respect the Ukrainian border.