Locog was forced to clarify its stance on the issue after its chair Lord Coe told the BBC anyone wearing a Pepsi T-shirt may not be allowed access.
Coca-Cola and other sponsors had spent huge sums on the London Games, he said, and their rights must be “protected”.
Organisers have pledged to clamp down on attempted “ambush marketing”.
Under International Olympic Committee (IOC) rules, tier one “worldwide partners” – such as McDonald’s and Coca-Cola – get sole global marketing rights within their sector, including being able to sell their products and services exclusively within Olympic venues.
Firms such as Adidas, British Airways and Lloyds TSB are 2012 Olympic partners, granting them exclusive marketing rights within their product sector in the UK.
Other 2012 supporters and suppliers with exclusive contracts include Heineken, Cadbury and Deloitte.
In an interview on the Today programme, Lord Coe said the London Organising Committee (Locog) had to raise a “mountainous” amount of money – some £2bn – through sponsorship and the rights of its partners during the event must be protected.
He was pressed by presenter Evan Davis about whether he could, for example, attend an Olympic event wearing a Pepsi t-shirt.
“No, you probably would not be walking in with a Pepsi T-shirt because Coca-Cola are our sponsors,” he replied, adding that Coca-Cola had invested millions of pounds both in the Games and grass-roots sport.
In an increasingly testy exchange, the BBC presenter then quizzed Lord Coe on whether he could “go in with Nike trainers on?”.
“I think you probably could…Let’s sort of put some reality in this. You probably would be able to walk through with Nike trainers. Does that satisfy you?”
Locog later issued a statement clarifying its position, saying that “any individual coming into our venues can wear any item of clothing, branded or otherwise”.