There are several ways to turn closed-end pens. Pin chucks work well and are easily made in the shop - you don't have to buy them. All you need is a length of steel or aluminum rod (available at most Ace Hardware stores as well as the big-box stores). You need a rod that is very slightly smaller than the ID of the bore of the pen (or the pen tube if there is one). File/grind a flat on one side, and then cut the head off a nail whose diameter is very slightly less than the depth of that flat. Put the nail on the flat, slip the rod into the blank, and give it a quarter turn - the nail will roll to one side and wedge itself against the inside of the blank, locking the blank to the rod. Mount the rod in a collet chuck, or a Jacobs chuck, or even an ordinary scroll chuck with pin jaws. If you are using a pin chuck, you don't absolutely need tailstock support although using the tailstock is never a bad practice.
Alternatively, you can use a length of steel rod without the flat as a sort of jam chuck. This is where the article you read suggests using masking tape to pad out the diameter of the rod. However, if the rod is sized just slightly thinner than the bore in the blank, you don't need tape. However, you do want to use the tailstock to apply axial pressure on the blank while turning it to size and sanding, and then finally part off the tip of the blank. You will have to either hand-sand the end, or use a sanding mandrel to finish off the end, but that's not a big deal.