How is that a Nazi connection la 

It's purely because of Olympics rules and regulations, i think it was mentioned that one the shirt of the coutnry's representatives, There can only be 1 logo of the brand sponsor. Since the 3 stripes is also considered a brand logo by Adidas themselves (the 3 stripes are trademarked), therefore they cannot have that on the shirt. Adidas shirts are only allowed the 1 logo on the chest.

I think the same applies to Puma, if u realize Puma shirts usually have up to 3 logos of the puma on the shirt (on the body and then maybe 2 on the sleeves etc). For Olympics there can only be one makers logo so modification or a different shirts also have to be used.

Sometimes, The maker for Olympic football's team shirts are not the same as what they usually wear in other tournaments. An example is Australia who uses Nike, which is contracted to the Football Federation of Australia. However the maker that sponsors Australia football contingent in the Olympics is Adidas, so during the Olympic the Australia mens football team wore Adidas. This is because in Olympic the players represent the country Australia, and not the Football Federation.

This info is something from the back of my head, i think i read it somewhere during the 2008 Olympics. So do correct me if any of the info is wrong. I've attached an image of the stuff ive mentioned above, a picture of Australia vs Ivory Coast. Notice that Australia uses Adidas, and there is no 3 stripes. As for Ivory Coast, they used the slightly modified version of their 2008-2010 shirt, if you notice the white puma logo on each side of the shoulder is absent during Olympics.

Sepang, Malaysia  11/02/2011  8:30 A.M.  Departure Scan
Shah Alam, Malaysia  11/02/2011  6:58 A.M.  Arrival Scan
Sepang, Malaysia  11/02/2011  6:58 A.M.  Arrival Scan
Shenzhen, China  11/02/2011  3:29 A.M.  Departure Scan
Sepang, Malaysia  11/02/2011  12:09 A.M. Package data processed by brokerage. Waiting for clearance. / Released by Clearing Agency. Now in-transit for delivery.
Shenzhen, China  11/01/2011  11:37 P.M. Arrival Scan
Koeln, Germany  11/01/2011  5:13 A.M.  Departure Scan
Sepang, Malaysia  11/01/2011  10:49 A.M. Package data processed by brokerage. Waiting for clearance.
Koeln, Germany  11/01/2011  12:11 A.M. Arrival Scan
Castle Donnington, United Kingdom  10/31/2011  10:00 P.M.  Departure Scan
Manchester, United Kingdom  10/31/2011  6:44 P.M.  Origin Scan
United Kingdom  10/31/2011  7:43 A.M.  Order Processed: Ready for UPS