galaxy - Do all the stars visible to the naked eye belong to Milky Way?

For decades the variable star S Doradus, in the Large Magellanic Cloud, was considered to be the most intrinsically luminous star known. But even though the Large Magellanic Cloud is the second or third closest external galaxy, S Doradus is still too far away from Earth to be seen with the naked eye from Earth. O fall the stars that always or sometimes are intrinsically brighter than S Doradus, only the variable Eta Carinae, in our own Milky Way Galaxy, is close enough to Earth that it is sometimes visible with the naked eye.

Omega Centauri, or NGC 5139, was cataloged as a star by Ptolemy in his Almagest about 150 AD and by Bayer in the Uranometria of 1603 - Bayer named it Omega Centauri. It is at a distance of about 15,800 light years from Earth. There is a theory that Omega Centauri is a remnant of a dwarf galaxy that as captured by our galaxy.

Thus Omega Centauri is an object that was listed and named as a star and may be the remnant of a former galaxy that has been captured by our own galaxy. Thus so far it seems to ALMOST fit the definition of an extra-galactic star visible from Earth with the naked (Human) eye.

Of course Edmund Halley noticed that Omega Centauri was not a star as early as 1677. Today it is classified as a globular Star cluster in our own galaxy (and possibly the remnant of the core of a dwarf galaxy). The light that makes Omega Centauri visible to the naked eye on Earth comes from the light emitted by hundreds of thousands or millions of stars, not one single star.

Even though a globular star cluster has the light of tens of thousands to millions of stars, and our Milky Way Galaxy has over a hundred globular clusters, only a few of them are visible from Earth with the naked eye (47 Tucanae mentioned by RichS is another, and it was also mistaken for a single star at first).

So a single star that was as far away as Omega Centauri 15,800 light years away, or 47 Tucanae 17,000 light year away, would have to shine as bright as tens or hundreds of thousands, and maybe even millions, of ordinary stars to appear just barely visible to the naked eye like those two clusters.

The Canis Major Dwarf Galaxy is believed to be 25,000 light years from earth and the nearest external galaxy, if it really is a galaxy. The Saggitarius Dwarf Elliptical Galaxy is about 70,000 light years from Earth and the Large Magellanic Cloud is about 163,000 light years from Earth. A star in the Large Magellanic Cloud, about ten times as far away as Omega Centauri or 47 Tucanae, would have to be as bright as millions to hundreds of millions of ordinary stars to be seen by the naked eye from Earth.

I suppose it is theoretically possible that one of the only about 6,000 stars visible with the naked eye from Earth might actually be in one of the 2 or 3 closest galaxies or floating alone outside of the disc of our galaxy. But it would have to be a supergiant or hypergiant star, and astronomers would have to somehow not notice oddities in its spectrum that would point to it being so rarely luminous.

I would estimate that the odds against that would be "astronomical".