I agree with my colleague ... use the 'real' date of 1 MAR 2013.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
This should not make a big difference. Put the date stamped on your I-94 Card by CBP.
You can provide both documents and explain that this is the same date because of leap year.
Garmo Law Group, PLLC (Michigan) 248-626-0050. This advice is only general in nature and does not constitute an attorney/client relationship. Speak to an experienced attorney before making decisions.