Speaking of the original question - when I bought my first AS it came with a lug wrench that the PO had bought. So I never thought about it again.
That is, until I tried to use it on the side of the road; the "sockets" were too fat to fit around the lug nut and between the center chrome hub cover. I always carry a pretty full wrench and socket set, so I had a good plan B, but that could have been a real problem. So yes - you must be careful about which speed wrench (lug wrench, cross wrench or even socket). Test them before you need them.