The two big errors in the title arise from the assumption that Engagement and Relevance can be separated. Engagement without relevance is SPAM! and Relevance without Engagement is pointless. So why would you ever imagine them being at odds or even separate. The answer to that I believe lies in the author's background and also provides the clue to the huge and 3rd error in the article. The author's background is in PR. I have long held that PR is a great profession (I believe the second oldest) but because of its assumptions and processes it is diametrically opposite to the requirements of social media. PR is about constructing and controlling the message and social media is all about engaging, influencing and participating. We see too often social media campaigns fall into crisis when PR companies take the reigns. This is no fault of theirs, it is just how they were taught.
The 3rd and hugest error is the POV the author takes about Engagement and Relevance. The assumption is that engagement and relevance is a factor of how useful the customer is to the brand. This is very PR thinking. Social media is customer centric and therefore the question is always how engaging is the brand to the customer and how relevant is the brand's content to the needs of the customer. Not the other way around. PR and Social Media are brilliant partners when they stand side by side. But if PR steps into the shoes of Social media a trip and fall is not to far off. Once again it is not their fault because they were taught this way. But brands that go shopping for agencies should be aware of these easy to spot errors and plan accordingly.