No, but that little circle is centered above the groove I am referring to.
One day I used an opener to tear the plastic/crimped aluminum top off a vial, and accidentally took the whole top off, rubber stopper and all. On my vials, the inside of the rubber stopper is actually 2 separate protrusions, with a groove in the middle that runs full width.
By going inline with the groove, you can aim the needle at the side of the vial, while only having to pierce the thinner section of the stopper.
Mine looked like these below. If you go diagonally in the wrong direction, you have to pierce 1/2" of rubber. Not good.
But in searching for an image I see that there are other stopper designs as well. Guess you gotta look carefully at your vials before reconstituting.
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