Windows will not be able to report if you are running a 32-bit version of Windows on a 64-bit machine. It will only report that you are running a 32-bit version of Windows.
You can determine if you are running on 64-bit capable CPU by using CPU-Z, using the instructions below:
Download and run CPU-Z, and look at the CPU tab.
Look for the line labeled Instructions.
If EM64T is displayed, your processor is 64-bit capable.