I have to agree. If it wasn't you that bruised the taper out of spec it was someone before.
On my square taper bikes I find that the bolts are always less tight than I leave them but the arms are still jammed on. It's like on a proper fit taper the arms actually walk themselves ONTO the taper rather than off. Only a deformed taper socket in the crank would walk itself off like this.
And yes the taper angles are all universal.