Have you ever had anyone tell you they homeschool during the summer? Not just saying that they keep their kids doing educational workbooks so they don't back slide, but claim to be homeschoolers because they do the summerbridge stuff over summer break.
It doesn't bother me. I look at homeschooling as a multitude of different ideals, possibilities, and different outcomes. A homeschooler, in my opinion, is anyone who teaches their own child. Doesn't matter to me how long they do it for...whether it is for the whole year, or just the summer. Home education doesn't have to be a full time endeavor.
I am happy when I see families getting involved with their child's education. When I was a kid, school was at school, and home was just play. I think it is fabulous when parents are proactive in helping their kids to learn through the summer.
I am a homeschooler, but I don't see anything specifically wrong with public school. It just doesn't work for my family. For other families, I know it works well. If they choose to continue education over the summer, then yes...it is home school.