It usually does. But I think such parents have distorted perception. When parents were blue-collar kids, they studied at lower-grade schools, and with some persistence could get high grades. This allowed them to get to university and move up by social ladder. (Even though, there's been a trend that more % of people get higher education.)
And then they set much higher standard for school, sending children to where it's really hard to get all A-s, even though the kid performs pretty well, way above the nation average.