Yeah - I was quoting the velocity definition given by an article pointed to by TFA. But I mostly agree with you, especially about the identification of business value. My point was that it’s better to have a value that can be measured by the participants (ie, productivity), than one that can’t (business value).

That said, while I am no fan of “agile as popularly understood”, my experience suggests you have the causality backward. Agile is simply a term forced on traditional project managers to make the business sound cool. Nothing is different from the way it was before agile, except the meetings have cool names.

In an environment that takes the agile manifesto seriously, working hand in glove with the business is kinda the point. But most businesses haven’t even heard of the manifesto, and those that have … don’t care.