The main question to ask is what was stopping you from being able to get that stud all the way in?
Obviously the proper way to install a stud is to press it into the hub. On vehicle that can be accomplished with a stack of big washers and a wheel nut, you tighten the wheel nut and because of the washers being in the way in between the nut and the stud, the wheel nut as it's being torqued harder will pull the stud in, that's how I replaced studs on my CTS before.
Get that stud taken care off then go back to your wiggle test.
Obviously the proper way to install a stud is to press it into the hub. On vehicle that can be accomplished with a stack of big washers and a wheel nut, you tighten the wheel nut and because of the washers being in the way in between the nut and the stud, the wheel nut as it's being torqued harder will pull the stud in, that's how I replaced studs on my CTS before.
Get that stud taken care off then go back to your wiggle test.