You're not allowed to buy, posses, or drink alcohol before 21, regardless if you're in Kentucky or not.
"Twenty-one states have no laws prohibiting those under 21 from drinking alcohol. 1 Contrary to popular belief, the National Underage Drinking Act of 1984 does not call for states to enact laws against underage drinking, but only against the purchase and possession of alcoholic beverages. The states with no age prohibition are:
California
Connecticut
Florida
Georgia
Hawaii
Iowa
Kentucky
Maryland
Massachusetts
Mississippi
Missouri
Nevada
New Hampshire
New Mexico
New York
Oklahoma
Rhode Island
South Carolina
Virginia
Wyoming
These states may charge persons who have consumed alcohol with alcohol possession or other violations in order to, in essence, enforce a non-existing law."
http://www2.potsdam.edu/hansondj/YouthIssues/1127406398.htmlI've seen it in a few other places as well.