> If you're denying people access to the system based on where they happen to be, it's not universal.
“Universal” seems to be a later construction, it was originally “unconditional”, and in both cases the writings on it for many years under either name made it clear that the reference was principally freedom from means- and behavior-testing, contrary to status-quo welfare programs, but that it would target a population based on (exact scope differs in particular proposals) residency, citizenship, and/or age. Not surprised that the “no borders” crowd has seen it differently, and their version certainly is a valid instance of the general idea, but they don’t get to rewrite history and narrow the scope of the broader concept to their new version.