No. Both methods result in the same $3588 refund. Doug even says so: "NOTICE, however, you are only asking for and getting a refund of the FITW,,, namely, 3588."
Using the "John DOH" filer grossing $800/week, $41600/year:

DOUG555 EXAMPLE:
41,600 + 3588 + 1747.20 + 603.20 = 47538.40
Line 21 has (47538.40)
Line 22 has (5938.40)
Refund of 3588.

NET PAY EXAMPLE:
Line 21 has (35662.)
Line 22 has 5938.
Refund of 3588.
http://jesse2012.com/JTD1040.pdf

Heavy is the head that wears a crown.