Real school? Mean teacher?

A strange conversation took place in my kitchen today. An acquaintance (she cleans house for us bi-weekly) was here today. We usually leave before she come because DS2 freaks out and crys when she arrives, even if she doesn't bring in the vacuum right away. I overheard the following:

Her: Is your mommy a mean teacher?
DS1: No, she's a good teacher.

Huh?

(It might have been "mean teacher or nice teacher" answered with "nice teacher". I kind of did an audio double-take, except it wasn't repeated.)

So while we were in the car, on our way to run errands, I asked DS1 about the conversation with her.
DS1: She asked me if I was going to real school or home school.
Me: What did you say?
DS1: I said home school.
Me: Home school is a real school, too. It just doesn't have lots and lots of kids.

Double huh?

I need to have a talk with this lady. She used to go to our church. We've known her about 3 years. It's nice that she talks directly to DS1 and will have a conversation with him (some adults don't talk TO kids, they talk AT them or act like they're not there). It just dumbfounds me that she'd ask if I were a mean teacher (I actually heard that part clearly) or if he was going to "real" school. Many non-homeschoolers that I know will question me about homeschooling, but this is the first time that I'm aware of that DS1 has been put on the spot. At least I know that he understands that he "goes to homeschool". I guess that's good, right?