It wasn't true when I lived there. I didn't even bother to apply to Lowell. Lick got the best, particularly out of Town Hall School (probably the best private grade school in the city at the time). Lick was then private and tuition free, with entry determined by compeitive examination only (it lasted three days). I remember nearly 20% national math finalists in just one class with large percentages of the graduating class going to what were (then) decent Ivy League schools. The student body was over 40% Jewish (I wasn't). It may be different now that Lick is charging tuition, but back then from where I went to grade school (which was Stuart Hall), you went to Lowell it was because you couldn't get into SI or Lick (a lot them went to SI because they were Catholic (I wasn't)).
The best public high schools in the area are not in Marin or Palo Alto, but in Lafayette and Moraga (Acalanes and Miramonte, respectively). Both Marin or Palo Alto are so infected with PC liberalism that the students don't cut it.
Lincoln (and Washington) are a great deal better than they look, even in test scores.
I'll stick to objective measurements, thank you.
The main failure of the school district is that it does a very bad job in general with black and hispanic students, even compared to the California average. The black activists that complain about SF public schools have a genuine grievance, but of course they have no practical solution.
The welfare plantation strikes again.
Given the score distribution in districts with much lower private school enrollment (SF has double or triple the private school enrollment of any CA district); I don't think either Lick or SI are any better than Lowell - the number of potential high-scoring kids just aren't there in the population, and Lowell is huge for such a high-scoring school, it sucks up most of the available talent, even if you assumed that SF has the educational demographics of Marin or Palo Alto. How schools score depends mainly on the students. Add to that as far as I know SI is typically considered a backup school for smart kids that don't make it into Lowell, it just doesn't follow that either Lick or SI are any better than Lowell, there just isn't the talent pool in the population to make it likely.
I know Asian students do well in college, but only if your metric discounts the value of humanities. I'm sorry, but your last post appears to me to bear a thinly veiled parochialism in that regard, using the assumption of high competition among Asians as the lone determinant of quality (even when I was a kid, Lowell was considered "a Chinese school"). BTW, I'd put up my ten year old against many of those kids, even in math (she starts college calculus this fall). She's home-educated and won't waste her time with high school if I can help it.
The electoral problem in SF is the Asians don't vote, and municipal elections are won with a very low turnout. That means that even a small politically organized minority group, like gays or leftists, has a free ride.
Sounds like you have work to do.