No, I wouldnt bend the truth either. Dont say something you can't back up. I merely that you should be sure to mention any big name companies you do have relationships with.
Yup. The takeaway from our post is simple: if you're working with people from successful companies, mention them. If your lead engineer was a high-ranking team lead at Google, that carries more weight than if his latest work was, let's say, managing the database for a potato factory in Ohio.