Just some history. "Original six" is a misnomer. When the league began, there were four teams. There wasn't any season in which there were exactly 6 teams (sometimes more, sometimes fewer), until 1942, when the league consisted of the teams we know today as the original six. The league would remain that way until 1967, when there was prolific expansion. My assumption is that was because of TV. If you had been watching hockey for under 25 years, and that expansion happens, it's understandable that you might think of these teams as the original six, but more accurately they represent a legacy 6, or a pre-expansion six, or something.
Technically you are correct. However, these 6 teams are what is universally referred to as The Original Six by anyone who treasures hockey. Hence why I capitalized the title.