I'm wondering what kind of response you give your daughter when she says "I didn't play with anyone." Does she get sympathy from you? Or perhaps some special Mom-daughter time? The reason I'm asking is that if she, in fact, DOES play with other kids at school, there may be some "reward" she's getting for telling you otherwise. Just a thought.

More to the point of your question: You seem concerned about your daughter's ability to make friends and to be progressing in her social development. That's certainly something all parents want, especially with our kindergarteners. And you did the right thing to check with the teacher to find out what s/he has observed in the classroom and on the playground. the teacher indicates "No problem in the friendship department." So why are you still asking your daughter the question? By asking it repeatedly you may be giving your daughter the idea that her ability to make friends is a worry of yours and that somehow, whatever she's doing at school is quite "measuring up." I'm not suggesting you believe this, I'm simply suggesting that continuing to ask the question may be creating some anxiety in your daughter.

I suggest you give the question a rest.  

Instead, how about asking your daughter which of her classmates she'd like to invite over for a play-date. Then connect with that child's parent and arrange something. Keep the date short and fun and it's quite likely that your daughter will soon be volunteering information about who she played with at school.

I hope this helps!