From the looks of it, you don't need a receipt or the original box.
Here is the email I got from Nike within 5 minutes of submitting the e-claim form online.
Thank you for your Nike.com E-claim submission! We have set up a Nike
e-claim authorizing you to return your product to Nike for inspection.
YOUR NIKE CLAIM NUMBER IS: # X-XXX
RETURN INSTRUCTIONS:
1. Please review the Nike return process Terms and Conditions you previously
viewed at
http://www.nikebiz.com/e_claim/other.html. By submitting
a product for inspection you have agreed to all of the Terms and Conditions
described there.
2. Clearly print the address and claim number on the package EXACTLY
as shown below (please include your claim number!).
Nike R.L.C.
E-claim # X-XXX
26755 SW 95th Avenue
Wilsonville, Oregon 97070
3. Please include only the item you specified on the e-claim form. Remember,
only one product per claim number will be accepted.
4. Include a brief note with your name, home address, phone number, claim
# X-XXX, and a description of the claimed product flaw in the box
with the product.
5. Ship the package with an insured and traceable delivery service.
Nike assumes no responsibility for lost or stolen packages. Hand deliveries
are not accepted.
As a recap, upon product receipt and inspection, if the product is determined
by Nike in its sole discretion to have a material or workmanship flaw,
a NikeTown.com product voucher will be emailed to you with specific redemption
instructions. Note: Some swimwear, children's apparel, cycling, golf
products, and Jordan brand footwear may receive direct product replacement
instead of a product voucher.
If you have any questions please email us at
consumer.affairs@nike.com
or call 1-800-344-6453 for assistance.
At NIKE we strive to maintain high standards of quality in all of our
products. We are equally dedicated to providing quality customer service.
We appreciate your business and the opportunity to service you.
Thank you,
Nike USA Consumer Affairs