The fact of the matter is that everybody is right. Having your own product is great but it isn't absolutely necessary. Those who have their own product can build a website around that product and add affiliate links to it. Those who don't have their own products can still create a great website and be an affiliate marketer. Producers of products love affiliate marketers and products are not the least bit hard to find.
The thing that both those who do and those who don't have their own product have in common is that they both must be passionate about the products they sell. You will never be successful in selling something that you aren't interested in yourself. It takes drive and ambition to succeed at any endeavor and affiliate marketing isn't any different. You must be passionate about a product or an idea in order to keep your drive and ambition alive and well for the long haul.
Whether you are marketing your own product or a product produced by others your success is directly related to how effective your marketing techniques are, how focused you are, how well you manage your time, and how much you believe in the product.