Seems like the agent is confused; that's the line for a United Global First lounge, where only passengers in First (three-class cabins only, NOT Business First on a two-class cabin) are allowed access on their international leg portion.

I've used that United Lounge in Boston (drinking at 7am... thanks USA!) before, travelling economy on a UA flight (BOS-EWR-YYZ, ironically not on the international leg).