"The competitor had done all this work by going around the organization, interviewing the stakeholders, putting together presentations and data dockets that addressed their needs. This was work that Richard would have had to do otherwise. Thus, the competitor had helped Richard help him!"
This can actually backfire if it's not done very carefully and tactfully. Reaching out to multiple people in the same organization can also make it appear that you are just blindly going fishing. Those people will triangulate, and they'll talk, and they'll compare notes. You'll need to make very sure that you've actually tailored your pitch and conversations to each of the people you're approaching.
If you're just sending the same, cold-intro email to different folks in the same company, they'll find that out pretty quickly, and you're dead in the water. By the same token, if you've been cultivating a relationship with Person X, and then you reach out to Person Y, Person X might feel that you've circumvented him, or gone over his head, and then you've bred some resentment with him. Instead, try this: if you've made decent headway with X, ask him if he thinks speaking to Y or Z would be a good idea. He may say yes, and actually give you the permission. He may even broker those introductions for you, provided he really believes in your pitch. Or he may point you in a more productive direction, with different people that hadn't occurred to you.
I'm not suggesting that the author is recommending a clumsy, cold approach to multiple parties. Nonetheless, I've seen it done so many times -- both on the buy side and sell side of consulting -- that I feel it bears mentioning. The general advice in the article is sound, but putting it into practice takes a fairly deft touch.