No, you are absolutely right about the distinction, I didn't see it as useful since the article is dealing with calendars here, eg. time of event at some location. I don't think I've used time without a calendar so it seems a bit abstract to do so.
Every time you say "wait a second" you're using time without a calendar or a timezone. You're referring to a point in time as an offset (1 second) to "now" which is the point in time when you say it, and its the same point regardless of which timezone you're in, or whether there's a timezone change in between.