The term has a real structure behind it, but no enforced definition. That is the core of what you are observing.
In underwriting practice, value-add means the asset is priced on current income and you can close the gap between that income and market-rate income through physical improvements, lease-up, or both. The return thesis depends on that delta being real and executable. A fully leased building with a new roof has no rent gap to close through lease-up, and the cap-ex burden is already addressed, so calling it value-add is using the phrase as flavor rather than as a description of the return structure. The deferred-maintenance property with three vacant units could legitimately be value-add, but only if the rent-to-cost math works after you price in the actual cap-ex.
The assumption doing the most work in any value-add pitch is the pro forma rent on stabilized units. Agents routinely use top-of-market comps for the projected rent and bottom-of-market estimates for the renovation cost. That spread is where the thesis lives and where it most often fails. Ask for the specific rent comps they are using, the vintage and condition of those comps, and a line-item cap-ex estimate. If they cannot produce those three things in writing, the term is marketing language.
The risk you did not raise: your ownership structure matters here. Bringing an agent into a deal where you are a minority partner with an operating partner creates an information asymmetry question. If the agent is sourcing to your operating partner's preferences and presenting to you after the fact, the agent's fiduciary runs to the transaction, not to your specific stake. A real estate attorney should clarify what representation you would actually have before you bring anyone into your deal flow.
What does the rent delta look like on your Columbus asset between current leases and market, and is there a trigger in your operating agreement for capital improvements?