No, whole-language isn't in favor these days, but there are still multiple fads in vogue. The fads tend to be embraced by the public schools.
I've encountered math with no wrong answers many times in reviewing grant applications and (sorry to say) in presentations about (federally) funded projects:
see this example.
My main point is that public education suffers from unproven fads. There are a lot of other problems, as well, including poor financial management (e.g. spending $60 million on iPads when you're firing teachers), low expectations for subject expertise (which makes people susceptible to believing faddish ideas), and so on. Some of the problems are far less frequent at private schools (e.g. you manage the money correctly or you go under). Private schools can't issue bonds or have a referendum to raise taxes.
I'm not saying that private schools are all better, because I know they aren't. I'm saying that many people wouldn't pay for private schools if the public schools were better.
But most importantly in reference to the OP, public schools shouldn't be blaming private-school families for their own failures, any more than Apple should be blaming its users for problems with its maps app.
