You are correct. You don't need a Twitter Transcript as a Twitter Chat Host. And, certainly, you don't need one if you are not a Twitter Chat Host. There you go, problem solved. ;)
Also, you could create a transcript by capturing every tweet, using Tweetdeck, and embedding it on your site. That is the natural Twitter way of doing it and it looks really nice! But, I have done it and to capture every tweet in the order that they were tweeted (oldest at the top so it reads like a book would read).. well, it takes a lot of effort and a lot of time.
But, it is an option.
Or, you can hire use by subscribing to the customized Twitter Transcript Package Membership.