Yes, once your ready to drill, every now and then, like winning the lottery the offending object spins itself right out! When that happens, do a little dance and know that this will be a very good day!
If you are not too confident with the centre punch, you can also buy drill centering guides , these fit in the hole and a small drill bit passes through the middle thus ensuring a perfect centre !
Paul. Just my 2 cents, but if this happened to me, id use a bushing, drill thru with the pilot diameter(depth of full bolt thread legnth), then drill to the size for tapping incrementally, to the thread minor diameter size. The extractors the gents are mentioning(i have a set) I am not saying it wont work, not at all, but those extractors are harder than tool steel, meaning if you break it, its gonna take a pro to get it out.(I have an edm to burn the tool out)....maybe it will come loose as you are drilling and retapping wont be necessary (using the lefty drills).