> No. As far as I can tell, approximately 100% of people in New York want to be tested, for many different reasons. You're assuming something and projecting it as truth.
In NY, the issue was not about wanting to be tested, it was about "are you there when they're picking people to test"; quoting from the article, which is very thin on info, people were selected "at 40 locations that included grocery and big-box stores". (In Santa Clara, with the Facebook ads, people "wanting to be tested" by going to a testing center is not anywhere close to 100%.)
The assumption that people who are at grocery and big-box stores are representative, infection-wise, of the population of a whole is not obviously true to me. Many other posters in this thread point out reasons why they might be more likely to be infected.
> But by your own logic, there can be no "random sample"...we can't tie people down and force them to be tested
This approach may go against American sensibilities, but other states (SK, DE, IT) have had better luck with the approach of sampling everyone in a town/region/area. Or at least pick people truly at random, not just a random sample of people who happen to show up in a public place in the middle of a pandemic with a shelter-in-place order in effect. (Also, I'm not sure how "my own logic" makes any claims about the impossibility of a random sample, could you elaborate?)
Even in America, you can at least try to account for the ways in which your sample is likely to be different from a truly random sample. The study by Stanford in Santa Clara county I know at least tried to do this, but of course you can't account for "thinks is infected" as a demographic attribute because that's the dependent variable; I don't know if the NYC study did this type of accounting, but I assume they tried to too.
> The truth is, the New York study did pretty much what we always do to get a random sample: asked a bunch of people at random to participate in the program.
You clearly know about sample bias, so I'm not sure why you think going to a single location (or even 40 single locations) and randomly asking people to be sampled is a good way to get a random sample. Think about going to every Costco and Whole Foods in the state and asking "people at random" for their political views. You're going to get a biased sample, even though you're nominally asking people at random. You can try to account for bias, based on demographic factors you observe in your sample that correlate with political views, right?
But we don't know enough about infection rate to be able to effectively account for infection rate given that people who are showing up at grocery and big-box stores on a random day are more likely to be exposed (they're at a store!) and thus more likely to have been infected than the population as a whole? Literally the only info you have is that they're more likely to be infected -- there aren't well-established demographic correlates with infection.