This was absolutely “bread and circuses” from the Mrs. Bill campaign. Total setup - girl was a neighbor and likely her parents have at least become acquainted with Chelsea and/or her husband. Damage control - they needed to show not only a vibrant Mrs. Bill, but her “softer side.” Most likely this was pre-arranged, quick call to the neighbor asking if their daughter would like to meet Mrs. Bill and then clearing it with the SS agents that they could let the little girl through.
The real question should be why the media followed up on the little girl and found out who she was and interviewed her - while not following up on who the women were with Mrs. Bill when she collapsed. Speculation that it was her doctor could have easily been verified or debunked, where was her doctor at the time? If it was the former aide, what was she doing that appeared to be a neurological test (squeezing fingers...)? How would the aide describe her “stumbling”? The media is absolutely absent - but for a bystander with a cell phone camera we would know nothing. But Karma to Mrs. Bill on 9-11 with a youtube video is so appropriate.