Unless you are talking about when they post a reply to someone else's question..... Yes, in that case, if they aren't sending it directly to the person who asked, you would see David's end of the dialogue, but most people on Twitter have figured that out and make public statements generic enough to be understood, or they RT the original question so that others see what they are replying too. If they send it as a reply to the person asking the question, only that person would see it, as well as others following you.
By the way. Twitter is a great place for up-to-the-second entertainment and news updates. You can follow TVGuide, or EW, or CNN or FOX news ...... not just friends and celebrities

Here are a few of my favorites:
RoushTVGuideMag
TVGuide
EWAusielloFiles
feliciaday (Felicia is the Twitter Queen! She often will also post Twitter tips)
Al Yankovic alyankovic (Very fun, PG rated humor. Often posts pics)
Daniel the TV Addict theTVaddict
aly denisof alydenisof (Allison Hannigan (willow on buffy).Lately she's mostly been posted cute pics and news of her new baby with husband Alexis Denisof (Wesley on Buffy)