They do, but the part at the bottom gets frozen, so many people (especially children), tip the cup up to get that part out. Some of the slushy is completely liquid and drips past the frozen part. Then they get brain freeze which may lead to some clumsiness.
If this was an adult person, this would be different. But, she is five and probably drinking in a moving vehicle. Also, i am not going to do a poll or anything, but i have a feeling anything blue is more popular with children than adults. Moo
The person who observed this worked retail and said they saw this staining on little children many times. This was at a pharmacy. The pharmacy did not sell anything like slushes.