I believe you are correct in your assesment. Tires made prior to 2000 used a 3 digit date stamp, 2000 and newer use the 4 digit stamp shown below..
Look for a long number that is stamped into each tire. It will start with DOT. With 2000 and newer tires, the last 4 digits will tell you the week and year the tire was made. Prior to 2000 a 3 digit stamp was used.
Example: Last 4 digits 2609 tells you the tire was made in the 26th week of 2009
It should look like the below pictured tire which was made in the 8th week of 2006
This kind of date stamping shown above started in 2000