I know my astronomy and whatever you wrote about quasars is half correct. Firstly, quasars are not quasi-stellar “objects”. They’re quasi-stellar radio sources, named as such because they were discovered through their strong radio emissions, but they’re visible in bright light, as you may know, too. They’re a part of the wide varieties of AGN, or active galactic nuclei. They’re not a “result” of the black holes, they’re “powered” by a supermassive black hole in the AGN’s core, which is surrounded by a monstrous accretion disk funnelling material in at a prodigious rate. The brightest quasars need to gobble up an equivalent of a thousand suns each year to keep the lights on. Whenever the AGN runs out of fuel which it needs to sustain the lights and emissions, they central region quietens down. Currently, the scientists are exploring the correlation between a galaxy and the mass of its central black hole. In particular, they are studying how the black hole’s role in gobbling up material eventually robs a galaxy of its chance to make new batches of stars. The central engine’s prodigious appetite seems to be causing its own eventual downfall as it runs out of fuel to keep accreting mass.
The reason which I believe the page mentions quasars as a “distant star” is because of quasar’s initial similarity to stars (emphasis on initial). They appeared bright, almost starlike, and their brightness would sometimes vary over a few days. However, it was hard to tell what they were associated with, and they were almost always very, very far away. eventually, Dutch astronomer Maarten Schmidt* (1929-*) looked at emissions lines from a quasar called 3C 273*. He pointed out that these lines were coming from energized hydrogen atoms and were highly redshifted (i.e., the spectra were shifted very far toward the red end of the spectrum). 3C 273 was not only very bright, but also very far away. Eventually, people realised that quasars are powered by extremely massive black holes consuming huge amounts of materials.
(*- Please note that I haven't re-checked the date(s) and the name(s). They might be incorrect, but I'm pretty sure I do remember them correctly)
So I think that it’s particularly common among the people who’re not familiar with astronomy to think of quasars as bright and/or distant stars. A mistake which needs to be rectified.
That’s all from me. Cheers.