That's absolutely wrong, Christopher. The tweet is public, your names (screen name and user name) are a part of every tweet. The time it was posted is fuzzy... you see "x minutes/hours/days ago" instead of a timestamp. Of course, if it says "4 minutes ago", you know exactly when.
example, off a random hashtag search:
screen name: sl33stak
user name: Jamie A MacDonald
@TechCrunch I prefer MY #Kickstarter project of #Detroit http://kck.st/e93ANp Well..If you're into #Photography anyways.
7 minutes ago via Echofon