You're both right.
I've been using plugs for at least 20 years. The type I use are plugged from the inside. I do always try to get whatever caused the leak out of the tire first. Some plugs are designed with a patch attached. These plugs are used just like a traditional repair where the tire is taken off the rim and buffed around the hole, then glued before the plug is inserted, and stitched, (run over with a patch roller) and the excess plug is cut off flush with the tread. This type of patched plug is usually considered a better fix.