I had a very similar experience! The person who lives across from my backyard came to my door one day telling me she was happy to find a babysitter in her neighbourhood and would bring her daughter in the afternoons No matter what I said to her about having limited spaces, being full, not taking part-timers, she kept insisting she was just so happy that I was in her neighbourhood! It was the weirdest experience, but like others have said, she was desperate and was trying to bully me into taking her child.