In broad strokes, that’s how I’d define it as well but, as with many things, there are devils in the details.
Should it be only “citizens” or should it cover all “lawful, permanent residents”, “anyone lawfully present”, or “anyone who can get themself into the covered territory”? If it’s only citizens and excludes mere residents, is that “universal”? [and in that case, this puts non-citizen residents at a huge disadvantage]
Should all care be covered, in unlimited amounts? Only well-accepted, standard care? Or experimental treatments as well? Should expected life outcomes (either absolute or relative among the possible care plans) be factored into the approval process?
Should public-paid care be metered in some way, with supplemental or elective care being paid out of pocket?
Should healthcare-adjacent services be covered? (independent living, assisted living, or nursing homes, or travel to medical care [routine commute, ambulance, or medevac])
Who defines what “undue financial burden” is?
It’s easy to imagine two people both strongly being “for universal healthcare” and disagreeing on many critical details.