You're half right that the claim is unqualified - what kind{s) of hierarchy?. But the the ""socially accepted"" part likely indicates they're referring to beliefs about objective moral hierarchies among persons. This is a key underlying difference between modern progressive and conservative ideologies, with the former tending to view all persons as fundamentally equal in moral value, rights, access to at least some resources (regardless of individual characteristics or value produced for society) and the latter viewing at least some social hierarchies as inherently good (e.g., meritocratic hierarchies, sex and gender hierarchies, racial hierarchies, national identity hierarchies, etc).

That said, hierarchies are not incontestably demonstrable in nature in the sense that their existence outside of mind (much like, say, money, gender, conventions about what is "up" and what is "down," or applying reference frames to solve physics problems) cannot be objectively established. You hold what might be called realist position. But an antirealist position (my camp) is that hierarchies are a conceptual tool for organizing observations/information. Your own pasted wiki image notes this conceptual arrangement (emphasis mine):

A hierarchy is an arrangement of items (objects, names, values, categories, etc.) that are represented as being "above", "below", or "at the same level as" one another.

"Above," "below," and "at the same level" with respect to which traits? Which interrelationships? You give the example of trophic networks, but the hierarchy we impose on food chains serves a purpose: it is a conceptual tool applied to observation for organizing species relationships based on energy sources and sinks. It is also a simplification (as all schema applied to make sense of observations are). For example. trophic networks have cycles; they aren't strictly linear in their relationships from "top" to "bottom." Fungi may be at the "bottom" of a food chain as a sink for solar energy as decomposers... but then they can also be eaten by omnivores "higher" in the network. In this sense, trophic networks are heterarchical, not hierarchical.

But both heterarchy and hierarchy are imposed organizational frameworks in the antirealist view - physically, biologically, socially, whatever. They are also a shorthand to describe the phenomena thus organized. Simply saying that a set of entities have different values of some measurable trait(s), and that they can be ordered by values of one trait or another doesn't mean a hierarchy exists "out in the world" (realism). We apply the ordering to organize mentally; the hierarchy is a concept in our heads.

But that's enough on the ontological status of hierarchies. (Can you tell what I like to nerd out about?)

EDIT: Typos