I don't quite see what all the confusion is about. Think of it this way. Suppose in June 2001 you bought a new car for $20,000 and paid 7% sales tax ($1400.00). Then, your State decides 7% is too much, and changes it to 6%, EFFECTIVE 1-1-2001. So you've overpaid by 1 %, and get a refund check for that amount ($200.00). If you bought another car in 2002 for $20,000, you would only be charged the new 6% sales tax rate, or $1200.00. So, beginning in 2002, you actually pay the correct rate, not the old rate.
Basically this is the same with your witholding taxes. The tax tables for 2001 are going to overwithold you because they're witholding at a higher rate (in our example 7%), but should be witholding at a lower rate (say 6%). So instead of keeping YOUR money for a year, they are giving it back to you now, before you even file your taxes.
As far as seeing it in your paycheck as of July 1st, that only affects the part of your taxes in the higher bracket (say 28% going to 27%). The part of your wages being taxed at the lower bracket (15% going to 10%) are not being moved for witholding purposes until 1-1-2002. So, beginning in January you'll see a reduction in your witholdings.
The tax reduction is REAL. The $600 represents money that you WOULD have paid in taxes for 2001, but now you're not. For 2002 and beyond, you'll actually see your witholdings going down.
If there was no change in your income or deductions from say 2000 to 2001, and this year you paid $200 at filing time (for fy 2000 return), then on Apr 15th of next year you'd expect to pay $200 again for fy 2001). In each case you underwitheld by $200 per year. If there were no tax reduction, you simply would be paying that $200 again, as always, and not think anything of it. That's exactly what it was the previous year.
Now, consider that all that is the same, except you've also got a $600 check in your pocket. THAT my friend, is a tax reduction.