This implies it's okay to have multiple websites for a business, but you need to have one "official website" for a business.If you want to ensure that your preferred website appears on the listing, you should make sure it is the only official website for your business across the Web.
Profiles and publisher mark up is something totally different.If I am reading this correctly, this means that you should not have 2 different websites in your Google + profile. Is this correct? If so how would you get 2 websites with Markup? Have 2 different Google + accounts? What about if you own 2 different URL's and have contributor to for both of them. Would that be a red flag also?