It can't do either.
If it came down to market forces to determine if PBS was on the air, it would go away rather quickly. It's only on because of tax dollars and funding by the rich who subscribe to its politics. Take both of those away and you may hear complaints but the ratings will be insufficient to keep it on the air and therefore those who loved it would lament the loss of such high quality programming but have no recourse.
Other than you being totally, completely, and unequivocally wrong, I would agree with you.
It is the donors and corporate underwriters that support it. And why do they do that? Because of the high quality of programming. And, because that quality brings in the dollars, it indeed stands on its own. (even if they don't produce crap like...oh...I dunno...Lost.)
If broadcast networks, or almost any number of national "cable" channels, were to rely solely on viewer financial support, how many do you think would actually stand on their own? I don't remember the last time I even watched ABC. I only watch NBC for two half hour sitcoms, and CBS for Letterman. Occasionally Fox when my wife forces me to watch Idol (against my will, I might add.) Otherwise, it's only a handful of "cable" channels and some HBO OnDemand.
Oh yeah, and a fair amount of PBS (HD OTA). Very few shows can compare to Nova, Nature, or Soundstage. Even the formerly educational Discovery channels have turned to crap with reality shows. And, now National Geographic is joining suit, calling themselves NatGeo. I guess Americans are just too dumb to pronounce "National Geographic" in its entirety?
One of the best, if not THE best, HD channels in existence is PBS HD. And, I think you find that I am not alone in that assessment.