I suppose so, but not exclusively. Private schools locally are several thousand dollars, and overseas are about 40k annually. Those that can afford the private school, with classroom ratios of sometimes 9 students per teacher, have a better chance of seeing their children educated. Public schools often have up to 32 students per teacher, which means about 1-2 minutes per student per class - if they're lucky. Many students slip through the cracks.
Public school teachers are overworked, and often desperate to obtain permanent certification and jump hoops. They over extend themselves, are climbing all over each other to get ahead, and often the student is a low priority. Once teachers have their permanent certification (anytime after 2 years), they are tenured, and basically cannot be fired without doing something criminal. Public school teachers are not all bad, but the good ones are few and far between.
Public schools typically have a no fail policy until the student reaches high school, so parents often don't realize that their children can't spell, do cursive writing, or divide until grade 10. Parents that can afford private school often choose that option because they realize their children have learned nothing in public school - that is, the children need to learn or their life long opportunities will be handicapped. Given the choice of spending 40k on a new car, or their child's education, they choose education.